Think of the Amalfi coast as small towns and villages, rather than cities. Sorrento the biggest place in the area, but not actually on the Amalfi Coast, just near to it. It’s also either very hilly, going inland, or the coast road which is flatter but gets very busy indeed. I’ll echo @Barry_L_i_p_t_o_n 's advice to skip the car. Driving is possible, but only for the gregarious yet calm / skilled, and ideally with plans heavily adjusted to take advantage of the car, which might take you away from the more normal tourist attractions.
for 4-5 days, it’s a no-brainer. One single location, and if you can’t find plenty of easy and interesting day trips, you’re not looking hard enough 
Big choice will be whether you want to explore or relax.
For the latter, places like Capri or Ravello are fine choices, and allow you to relax in those places once the day-trippers depart. Ravello is certainly a most peaceful and relaxing place in mornings and evenings, be it in the central square, or finding one of the many beautiful places to look out over the wonderful view of the coast, and the slow criss-crossing of boats.
For exploring, somewhere on / near the coast road is ideal, and the SITA buses are good/frequent, and allied to the ferries, give great transport options. In addition, walking is a rather under-utilised experience here. with an amazing criss-cross of paths that used to allow locals (and their donkeys) to get around, but that they tend to use less now. The walks give wonderful views and also insight as you pass through tiny hamlets or past home-made shrines. Julian Tippett’s book in the sunflower series is invaluable if the walking appeals.
Options I’d suggest for convenience: Amalfi, as it’s a bus hub (and ferry stop); Praiano for somewhere a little quieter, but still on the coast road; Minori if you like flat ground, or Positano if you are happy that walking to the restaurant will generate an appetite. For organised day trips, L’Altracostiera in Amalfi have been there for decades, and as well as running day trips, they’re also a local accommodation agency and (IIRC) travel agency for locals to see the world. They’re good.
If you want fancy hotels, then Ravello / Amalfi offer the fancier ones, that should still come in under that budget. Personally I much prefer apartments, which I put down to having spent too many nights in hotels through work, so valuing the extra space and freedom, but also loving grazing local food etc. shops and a broader desire to embed in the culture.
As you’ll be there in summer, I’ll give a shout out to quirky Atrani, where houses are built into the large viaduct that towers over this coastal village. That also means its square is generally sheltered from the sun, making it an oasis of cool on a hot day. Also recommended if it’s still there is the fish restaurant A’Paranza, whose degustazione menu was an extensive lesson in the differnt seafood on the coast, and when we were absolutely full, their remarkable lemon dessert was so light and refreshing, we were still able to eat it. There’s a nice energetic 20min walk from the stairs to Amalfi’s duomo to Atrani (or a less appealing walk alongside the coast road)
