One thing about the Amalfi Coast is that it almost doesn't matter which town you stay in as you are likely to spend a day in each. Staying in Sorrento is usually a good option for finding value. It's a larger city and has many hotels. I once stayed at the Bellevue Syrene (www.bellevue.it) and found it to be a smart splurge. Also, they have an easy-to-access jetty by the sea.
In Positano, the best classic hotels include The San Pietro (www.ilsanpietro.it) and Le Sirenuse. Both are very expensive, with room rates over $800 per night. Anything in Positano is going to be costly, however Buca di Bacco (www.bucadibacco.it) is a good value in town. Also, staying in Praiano at Casa Angelina is my smart luxury pick. It's luxe but prices are a good bit less than if it were located in nearby Positano.No matter where one stays on the Amalfi Coast, you will likely want to do day trips to Ravello (to see the gorgeous villas and gardens; there's a concert series there as well), Capri (need I say more), and perhaps Pompeii (for the ancient Roman ruins).
Italy is a top choice for Americans tourists, and surely the Amalfi Coast should be at or near the top of Italian destinations. It may be a long trip getting to the region but once there its hard to ever leave.
For general trip-planning information, see our Amalfi Coast Travel Guide.