It's the ultimate first-time Europe itinerary -- jetting between London, Paris, and Rome in a single trip. These cities are packed with sites, they're easy to navigate, and they offer a rich introduction to the continent. This trip is a must-do for any traveler, and it can be accomplished affordably and in a single week, if you plan wisely.

While we don't claim that this is an exhaustive itinerary, we’ve crafted one that gives you a manageable taste of three very different cities.

A Note on Flights

To make the most of your time on the ground, book a red eye (a flight that arrives early in the morning) on the way to Europe so you can hit the ground running when you land -- assuming, of course, that you can rest on the plane. For the rest of us, there’s espresso and sunshine.

For the most efficient touring, you'll need to book an “open jaw” flight, if you can afford it (they’re often a little more expensive, though not always). This means you’ll be arriving in one city, and departing from another, so you don’t have to double-back on your itinerary. In our example below, you will be arriving in Rome and flying out of London.

A tip for booking open-jaw itineraries: Use the "multi-city" or "multiple stops" tool on flight web sites when you search for fares. You'll often find much better prices than if you booked the individual legs of your journey separately.

Rome

Notes on Where to Stay: The historic center of Rome, where almost all of the relevant sights are (the Colosseum, the Vatican, the Trevi Fountain), is probably the most desirable area for first-time visitors, especially if you’re only staying a few days. The major sites are within a 30-minute walk, at most, and strolling is a pastime unto itself in Rome. Hotels in this area, however, tend to fill up far in advance, so if you’re booking your trip at the last minute, consider the Termini district, near the train station, for greater affordability and availability.

Hotels to consider in The Historic Center include Spanish Suite Campo de Fiori (rooms starting from $110). The Artemide(rooms starting from $250) is especially known for its excellent service.

Day 1: Arrival and the Ancient City

After you settle in at your hotel, head to the Roman Forum, and then to Palatine Hill. Rather than strolling around by yourself, consider investing in a guided tour, even if you don't think you're the tour type. There’s so much history here, but the narratives aren’t always immediately apparent. Rome Tours is highly recommended and is led by Classics scholar Daniella Hunt.

After your time atop Palatine Hill, make your way to the Colosseum. Make sure you buy tickets in advance for entry -- lines here are notoriously long. You can spend an hour, at least, wandering through the site. Grab an audio guide for extra enrichment, and make sure you make it to the second level for the views.

Watch the sunset from the Piazza del Campidoglio -- a well-known sightseeing spot that was designed by Michelangelo. For dinner, try one of the many homey restaurants on the small grid of streets behind the Colosseum, or enjoy a humble-but-hearty bowl of bucatini or one of the famous pizzas at Ponte Vittorio. From there, you can stroll along the Tiber, just adjacent.

Day 2: Trevi Fountain and the Pantheon

Start your morning with a counter cappuccino at famed Caffé Sant’Eustachio, where espresso is brewed with water from an ancient aqueduct.

Then, make your way to the newly restored Trevi Fountain and throw in a coin or two (over your shoulder, natch, to guarantee that you'll return) for good luck. Then onto the Pantheon -- a must see. Fit in some gelato and lunch (preferably in that order) while you’re at it. Gelateria Della Palma is excellent.

In the afternoon, head to the Piazza del Popolo, and end your day at the Piazza Navona -- a brilliant place to catch the sunset, if you time it right.

Day 3: The Vatican

On your last day in Rome, wake up early to enter Vatican City. Head on over to St. Peter’s Basilica, where you’ll likely have to stand in line for a security check. Entrance is free, unless you’d like to visit the top of the basilica's dome. If you’re interested in doing so, consider booking a tour, which will allow you to bypass the long lines.

After a bustling morning at Vatican City, enjoy a cafe lunch outside the Vatican museums -- Ristorante dei Musei is delicious.

After soaking up the sun a bit on the sidewalk, and maybe perking up with an espresso, wander through the Vatican Museums. Make sure to buy your tickets beforehand so you can skip the lines. You could spend all day admiring the grandeur of the Sistine Chapel -- if art is a high priority on your list, consider scheduling it earlier in your itinerary so you can come back, if you wish.

Finally, end your last night in Rome at La Pergola if you’re up for a splurge. This three-Michelin-starred restaurant does not disappoint, and the candlelit terrace and city view is almost worth the price tag alone.

Paris

Notes on Where to Stay: For easy access to Paris, a good place to stay is the centrally-located Marais neighborhood. Beyond convenience, it also represents a cultural nexus of the city, without the corporate glitz of the Champs Elysées or the touristy hype of the Eiffel Tower area (which is actually quite residential, apart from the area by the monument). Hôtel Providence Paris in the Marais is a chic choice, starting at only $170 per night.

If you’re looking for more of a budget option, steer clear of the Marais and check out the budget hotels and hostels in the Latin Quarter -- the historic student neighborhood and former haunt of literary heavyweights like Ernest Hemingway and Gertrude Stein. Be warned, however, that this area will feel touristy.

To consider when choosing a hotel: Paris is a small city, and walking across it takes astonishingly little time. The city-wide bike rental program, the Vélib, is also an excellent way to get around -- and nothing compares to the freedom of riding a bike in Paris on a warm day. With this in mind, don’t discount the possibility of finding a more affordable hotel in a less central area. The C.O.Q Hotel, for example, is a stylish new offering in the city that makes the most of its out-of-the-way neighborhood.

One last thing to consider: many restaurants and small businesses are closed in August, as that’s the universal month to vacation in the country. Plan your visit carefully if you choose to come during this time (though on the plus side, you'll find the city to be relatively peaceful).

Day 4: Arriving in Paris and Notre Dame

Catch a flight as early in the day as you can, so you’ll have a full day in Paris once you arrive and get settled. Carriers like Ryanair and EasyJet offer flights for as little as 30 euros between cities. For longer trips, train travel is recommended and enjoyable, but if you’re only here for one week, the airport (with all its hassles) is the fastest route.

Upon arrival, you should start where everyone starts -- at Notre Dame. It's worth the inevitable wait in line, and will anchor your entire Paris trip. Take time to wander back and forth over the Seine-spanning bridges, and through the alleyways of the nearby Marais. Stop for lunch at the excellent Middle Eastern takeout counter, L’As du Falafel.

Make your way to the storied (but admittedly overrated) Shakespeare and Company; play the bookstore’s rickety piano and maybe buy a postcard or two. Spend the evening at Le Centre Pompidou, Paris’s modern art museum with its inside-out design.

Finally, finish your day with dinner at Les Philosophes, which is famous for its French onion soup -- a dish many restaurants offer, but one that few master.

Day 5: The Louvre and Beyond

A Louvre visit is, of course, a must, and needs to be tackled first thing in the morning. Don’t deceive yourself that you’ll avoid the crowds, however.

In the afternoon, allow yourself to wander the nearby arcades, making sure to stop for macarons at famed patissier Pierre Hermé. L’imprimerie is a popular cafe usually busy with locals, and mains run no more than 20 euros.

Later, stroll by the Eiffel Tower -- the view from the top is iconic, but the line occasionally isn't worth it. The surrounding area is also overwhelmingly congested. A better way to enjoy the monument is to have a picnic on its lawns, or cross the bridge over to the Place du Trocadero. The view from here is particularly inspiring at night.

If you can afford it, treat yourself to a performance at the Opera Garnier in the evening. Just the building itself is a work of art, and it's free to browse the gilded lobby. Ask about same-day tickets, which can sometimes be purchased at a fraction of the price.

Day 6: Montmartre and the Musée d'Orsay

Reserve the morning for Montmartre, a neighborhood that once was its own windmill-filled village, and is known as the setting of the film Amélie. Its winding streets are a delight, full of curio shops and cafes. Arrive at the breathtaking Sacré-Coeur basilica and take in the views of the the city.

Nearby in Pigalle, the sex shops and their conspicuous advertisements aren't exactly family-friendly. That said, the neighborhood doesn’t feel dangerous, and the area has enjoyed a reputation for trendiness, rather than seediness, in recent years.

In the afternoon, visit The Musée d’Orsay, which many people describe as their favorite museum in Paris. It’s smaller, more intimate, and filled with natural light -- unlike the Louvre, which can feel dusty and dim on the inside.

If time and energy allow, walk along the Canal St. Martin and through the Belleville neighborhood in the evening. It’s a mix of up-and-coming young artists, Asian restaurants, and North African immigrants -- a picture of Paris's vibrant and dynamic future. Get a good night’s rest for your train journey to London the following morning.

London

Notes on Where to Stay: We recommend staying put in the area around Kings Cross/St. Pancras train station for your overnight in London. Not only will it make your commute with luggage much shorter, but it’s also a nonstop journey from there to Heathrow, Gatwick, and Luton airports.

The district is not quite as exciting or filled with sites as the West End, but it’s significantly more affordable. Kings Cross is also a short train (“tube”) ride away from major spots like Buckingham Palace, St. Paul’s Cathedral, and the bevy of museums in Kensington.

Stay at The Great Northern Hotel, starting at 189 pounds per night, which offers a true taste of London charm at a relatively affordable price (plus, you'll get tea with biscuits and jam every afternoon). If you’re looking for a lower-budget option -- it is just one night, after all -- check out the Clink78 Hostel, which offers private rooms starting at 65 pounds per night, and is clean and reliable. Another option is the London outpost of the hip Generator hostel brand. It also offers private rooms.

Day 7: Arrival in London and Trafalgar Square

In the morning, catch the high-speed Eurostar train -- they run every hour or so -- from Gare du Nord. You’ll arrive at St. Pancras station in London in a little under two-and-a-half hours.

After you’ve arrived at your hotel, take the tube to Trafalgar Square, a great place to begin. Walk down the mall to Buckingham Palace, which will most likely be swarming with tourists -- but it’s still grand, and a must-see.

After stopping for for a bite to eat (Portrait Restaurant in the National Gallery and Cafe in the Crypt are both convenient options), step into the National Gallery in the afternoon -- it’s worth wandering around for at least an hour. Don’t try to see everything; just pick one or two galleries that strike your fancy. If you’re really feeling ambitious, make your way to St. Paul’s Cathedral before 4 p.m., and be sure to buy your ticket beforehand for a discount.

Finally, head to The Quality Chophouse, not too far away, for a classically British meal that’s doesn't feel forced. Try the steak and the confit potatoes, and the terrines are also very good. It’s a great place to end your journey in London, and start dreaming about your next trip.