We stayed for 3 nights in early Sept 2014. We used an airbnb - depending on the makeup of the travelers and whether two of them mind sleeping on a couch that isn't 'private'...this is who we used...
https://www.airbnb.ca/rooms/326177?guests=4&s=PYlOusqX&sug=51
On the map it looks like it is in a funny spot, but it was a 3-4 min walk up the main street, up some stairs. We liked it - if you are carrying a lot of luggage, it's a bit of a pain as no cars are allowed up the main street (unless you are a resident). When we stayed (me, hubby and my mom) the owner's boyfriend met us in Amalfi and drove my mom and the larger suitcase around to Atrani. (He was going to a wedding and his car was full of stuff, unfortunately). The view is just of the buildings across the road, but I recall there was a terrace above with some chairs (but I'm not sure if they were for the apartment or another apartment). But the price is pretty darn sweet. There is a small kitchen and the bathroom was one of those 'open shower' ones where kinda the whole room (including the toilet area) got wet, which was a bit weird. I'm not really selling this place, am I?! (There was also a really annoying neighbourhood rooster who liked to crow as soon as the sun started coming up - I was ready to hunt it down and have rooster for supper). When we left, we had to cart our bags around to Amalfi to catch the bus. (Another reason to travel light!)
Anyhoo - it was about a 10 min walk around to Amalfi. There was at least one little grocery/convenience store where we picked up some food, a couple restaurants and a nice bakery where we would pick up pastries for breakfast. Amalfi has lots of restaurants and spots to buy food, of course.
Honestly, I hope someday we can return to the coast for 5-6 nights and I'd probably split my time between a larger spot like Sorrento and a smaller spot like Atrani...
If you want a place with a view, you're probably gonna have to up your amount willing to pay...