Meenamehta, yes..good idea to stay in either Amalfi or Ravello rather than Positano. You have a budget that is very good so I think in those shoulder seasons of spring and fall you can find a really great hotel in either town (I do not know Sorrento very well). I will look into my notes but for now, in Amalfi the nicest waterfront hotel would be the Santa Caterina and I am certain you would find rooms with great views there. (If you can get your hands on a used copy of what we used to call "the Bible," GOURMET TRAVELERS GUIDE TO ITALY by Fred Plotkin, you will find a lovely description of this hotel; the book is not only a food guide but it has a lot of information about Italy that you would not find in a regular "guidebook." (In a somewhat similar vein is the book by Carla Capalbo: Food and Wine Guide to Campania....very good reading and insight into a lot about this very special region of the world.
BUT the Santa Caterina is a bit of a walk along the main road to the town of Amalfi--not very long and it is pretty flat, but just be aware; maybe the hotel has a shuttle. Another classic older property is the Luna Convento, slightly out of the center but easy, flat walk. Both of these are in old buildings so rooms will vary a lot in size and view, so check carefully before selecting a room type. The other place would be the Convento di Amalfi, high on a cliff face but also not in the center. For this one, shuttle might be offered so check that. There are a few pleasant hotels along the sea, like the Bussola, which I think someone mentioned, above, and the Miramalfi; not as upscale as the first two I mentioned but very very nice even if they are not inside beautiful buildings. Easier walk to the center from these.
But, for the views, you really need to think about stying in Ravello. It's more of a small-ish village, much less bustling than Amalfi. Many day trippers but once they leave, so charming. Beautiful gardens with sea views....a gem of a place. The last time I was there I stayed at the Palazzo Avino (in a single room with NO view due to price). This is one of those perfect, old-World charmers and if you can handle the price--yes! The Caruso nearby is in that range and my sister loved her stay there (she took one of the view rooms!!)
But there are a couple of other Ravello hotels that are just wonderful--the Parsifal, Villa Fraulo, Villa Cimbrone....these are dreamy. I've not stayed in any of those latter hotels because I prefer being able to swim in a pool, but you would not go wrong based on the glimpses I've seen inside these properties and what I've heard from others who have stayed at them.
I seem to be going on and on.....let me know what you think and I will be happy to offer any advice I can.
You do NOT want to stay in Furore, or not at the Hotel Bacco. The restaurant is good, the hotel, no! There is an agriturismo hotel up there that gets great reviews but I don't think it will do for this trip. Furore is VERY high up with limited bus service and very pricey taxi rides to reach.
As for spring or fall.... difficult question. It might be too late to get the rooms you want for this spring, I don't know.
Based only on my own limited experience, early September is fantastic but crowded; later in the month the rain seems to come in and then skies clear up as you get into October. I cannot tell you how many times we've been disappointed by rain in the latter half of September--on Ischia for almost an entire week; in Maratea, same....on and on. But that's just my own tale and you know every year is different and the climate is changing perceptibly, so none of us can really predict. And as long as it does not pour buckets, you'll be ok, because you won't be spending your time on the beach....ok...gone on too long....will keep an eye on this thread!!