Base for Amafli Coast week

How many people? Please indicate the month of the year, and which year. (This is a far-in-advance booking destination.) Do you plan to do anything other than the Amalfi Coast, like Pompeii, Ischia, or Capri? Do you require a (pebble) beach and ocean swimming? Can you walk an unlimited number of stairs to get back to your hotel? What general budget do you have? Have you left time to get to your next destination or plane, from a relatively remote area?

IMHO, there is no single "best". It all depends on personal preference and what one intends to do during their week so you're going to get a variety of opinions. None of them are wrong unless they don't work well for planned daily activities, or can present issues getting around on foot if one has mobility challenges. Time of year can be a factor as well (when is your trip?).

Assuming it's during high or shoulder season, my pick is Sorrento for easy access to/from Naples, choice of transport for a variety of day trips (train/ferry/bus), quick, easy access to some attractions (e.g. Pompei via train) and range of accommodations, restaurants, etc. The main part of town is flat and easily managed on foot. While not 'on' the Amalfi Coast, it was plenty close enough for our purposes.

That said, you're going to get votes for Positano, Amalfi and others. There's some love for Salerno as well.

Editing to add: with a full week to spend, you could break your stay into two different locations. Worth mention is that if you are flying home from Rome, you'll want to stay in or near the city on the night before departure. This can be true for Naples as well if your flight out is very early.

I choose Sorrento as a base for three different trips to the area. Sorrento itself is a charming town (gets lots of cruise ship tour groups mid day in high season, but so does Positano and Amalfi). Sorrento is larger than those other villages, so more choice of lodging and eating in all price ranges. It's the easiest to get to being as it is on the train line from Naples (the local train) so arriving and departing are relatively easy by public transportation. If you are staying in Positano or Amalfi it's longer and more difficult unless you have a car/driver. Sorrento is also central for many day trips - Capri, Ischia, Naples, Pompeii - as well as Positano and Amalfi. The bus ride from Sorrento to Positano/Amalfi is a 'three star site itself' (according to Rick, and I agree) but it's best not when you are tired after a long journey and with luggage. In season there is also a boat - I always recommend taking the bus one way and the boat the other.
Having said all that Positano and Amalfi are a bit more 'charming' (I think Sorrento is charming as well).

Here's my trip reports (hotel details are in it) -
https://www.fodors.com/community/europe/amalfi-coast-rome-and-croatia-images-of-three-hot-but-wonderful-weeks-854867/
https://www.fodors.com/community/europe/july-in-the-mezzogiorno-3-weeks-in-southern-italy-amalfi-coast-and-puglia-1024327/

Photos are now at: https://andiamo.zenfolio.com/p266655284

Start with these two old threads, but there are plenty more - Search box top center:

https://community.ricksteves.com/travel-forum/italy/one-week-on-the-amalfi-coast

https://community.ricksteves.com/travel-forum/italy/how-do-i-get-from-pompeii-to-positano-is-there-a-direct-route

"Amalfi Coast" has a specific meaning, but it's not religiously observed. We stayed in Sorrento for five nights, simply because it's an ideal transportation center. It's NOT on the Amalfi Coast, but we didn't care about (pebble) beaches, and hired a car and driver for one day to see Positano, Amalfi, and Ravello. I would not want to have a car in any of those three places, and I wouldn't want to take my luggage on the SITA bus from the Sorrento Circumvesuvina station. For that matter, Sorrento has little parking, and closes some streets every night for the Passegiata. In high season, these places book up nine months in advance. In order to pick a town to sleep in, you need a list of places and things that are "musts" for you.

I wouldn't want to take my luggage on the SITA bus from the Sorrento
Circumvesuvina station

We stayed an easy walk from the station so no bus needed.

http://hotelantichemura.com

Hiking: a fun activity on Capri. Ignore the touts for tours on the website linked below as you don't need them. Click on each for how-to descriptions, and buy a map of the island at the tourist info center when you arrive.

https://www.capri.net/en/traveller-search?todo%5B%5D=nature&all=1

I've stayed in both Sorrento and Salerno. I liked Salerno better. Look at a map, most of the AC towns are closer to Salerno. From Sorrento, there's a lot of inland travel to get to the scenic coast a little west of Positano and the ferries have to go around the cape. To Sorrento, you use the slow, local commuter train from Naples. To Salerno there are frequent high speed trains from Florence, Rome and Naples. Salerno has an interesting historic center; Sorrento's is a lot newer. Salerno is mostly level with a large sandy beach.

If you want to visit Capri, Sorrento is better. For Pompeii, both are good, though Sorrento is better. From Salerno you can day trip to Paestum and see the beautiful Greek temple ruins.

You might also consider splitting your time, staying in Sorrento or Salerno for a few nights and 2-3 nights in one of the AC towns for hiking.

Here is another vote for Salerno. We flew into Rome and took the Frecciarosa fast train to Salerno. It is a transportation hub on the Amalfi Coast offering train, bus and ferry connections. It is not as touristy as Sorrento and offers more of a local experience. Every evening the locals will stroll the Lungamare seaside walkway. There is a charming Old Town that is fun to explore. We took the ferries in mid May to the other villages rather than deal with the crowded buses. The view from the water is breathtaking. There is a train that goes to Pompeii (the village station and not the scavi, but is an easy walk to the scavi site). There is also a train that goes south to Paestum. It is too far for easy access to Capri, but that was not on our list of must sees.

Would recommend B and B Salerno Centro. It is not far from the train station, and it is a wonderful Italian experience. Try to stay in the Positano room as it has every amenity as well as a private terrace!

If your plan is to stay for a week, then I suggest splitting your stay between Sorrento and an Amalfi Coast town. Sorrento is an ideal base to explore Pompeii/Herculaneum/Vesuvius/Naples and Capri. Stay on the Amalfi Coast the rest of the time to explore that side. There’s a lot of time and hot, frustrated crowds involved in day tripping all the way around the peninsula. You want long day trips to be at a minimum. Most people are day tripping into the area, don’t be one of them. There’s no shortage of things to do here.