Bed and Breakfast in Sorrento and Amalfi

Spent 2 nights each in Sorrento and Amalfi earlier this month. We recommend 2 hotels that are not BnBs but include very good breakfast buffets. In Sorrento, try the Palazzo Tasso. Good room and great staff. Right on the main pedestrian street very close to all the main attractions. Really a surprisingly good small hotel. Good restaurants - nearby Kebab Ciampa and close by La Fenice. Easy to get around in old town Sorrento as relatively level.
In Amalfi, we stayed at Hotel L'Antico Convitto, also right downtown. Has attractive rooms, reasonable rates, a really good elevator and top notch security. Owner/manager on premises. The main part of Amalfi is relatively easy to negotiate - especially compared to Positano.

Beckie - Hotels in Sorrento with great locations and near public transport:

https://hotelantichemura.com/

https://www.sorrentohotelmignon.com/

https://www.bristolsorrento.com/

Here is a good Airbnb in Amalfi:

https://www.dimoradelpodesta.it/en

If You are interested in spending less money You can also consider to book a b&b in Piano di Sorrento. It's just few minutes far from Sorrento but it's cheaper. Otherwise if You like to spend less i will reccomend to book a b&b from MassaLubrense to Nerano

Where you stay is dependent on what you want to do. (Note that your subject line suggests that you are going to stay in Amalfi town, but you mean "a town on the Amalfi Coast.") What I mean by that is that many people stay in Sorrento in order to take advantage of good transportation options. You don't stay in Sorrento for beach-time. If you stay in a town that also has a Circumvesuviana train stop (there are no such towns on the Amalfi Coast), and the train is an easy walk from your hotel or B&B, that's almost as good as Sorrento - but there may be fewer restaurant choices, for example. The Circumvesuviana is considered to be very crowded and very "gritty."

The Circumvesuviana is very good for getting to Naples, Pompeii, and Herculaneum. It you are going to Capri, you have to take a ferry from Naples, Sorrento, Positano, Amalfi (town), or Salerno. I mention that because you have to go to one of those towns for a ferry if you are not staying in one of those towns. It is a substantial distance from the Sorrento Circumvesuviana station to the Sorrento marinas. But there is a public bus.

If you want to go to Positano for the day, most people take a bus, either from Sorrento or from an Amalfi Coast town if they are on the AC. The AC busses require a change in Amalfi, if you are going to the "other side" of Amalfi. The bus from Sorrento to Amalfi (via Positano) runs roughly half-hourly, and is very cheap, but very crowded. In high season (when such a thing returns ... ), there are more people waiting in Sorrento for this bus than will fit on the next bus. If you don't use public transportation at home, you need to think about the time delays inherent in using public transportation.