There's da Costantino (via Montepertuso, 107, ph: 089875738).  The restaurant is family owned (the owner will even serve some courses of your meal). The starters (especially the antipasta plate) are quite good, though the ambiance is somewhat lacking (the place is very bright and is very basic). The prices are very fair as well. This place is out of the way and definitely beats the places on the usual tourist track. If you call them they will pick you up at your hotel.

La Sponda - this is the upscale restaurant in Le Sirenuse hotel.  Although pricey, the food is very fresh and inventive. Try the shrimp and scampi carpaccio which was individually dressed with lemon slices, sundried tomatoes, etc. Starters are about 30-euros, entrees are about 40-euros and desserts are 20-euros.  The ambiance was really amazing since Le Sirenuse has an amazing view of the beach, harbor and town below.  It is definitely special occasions place.  Don't forget to ask for a table on the balcony and dress code is casual elegance.

Max - this is a restaurant in an art gallery by the same name as you head down to the beach.  It's not cheap - the entrees are about 40-euros each.  The atmosphere is quiet and refined - it has a quiet garden and is located down some steps from the main walkway to the beach.

La Cambusa - this restaurant is by the beach, near the Buca di Bacco. The service is gracious and the restaurant had a good view of the main beach. Reasonable priced.

Champagne Bar at Le Sirenuse - Example of a dish: the seafood carpaccio with either Japanese condiments or Mediterranean condiments. They also offer other tartares like tuna and salmon, plus oysters.  The dishes are around 27-30 euros each.  The view is amazing - it's more relaxed than La Sponda.

(In Montepertuso - hill above Positano and a 15-minute ride from Positano)  Food in this town  can be better and cheaper than what you could find in Positano.

Donna Rosa  - this is a family establishment with the mom as the chef.  It's very refined food - very fresh and delicious.  Definitely a foodie place but at reasonable prices.  Dinner for two with 2 appetizers, 2 entrees and 2 desserts with drinks runs about 110-euros. It's a beautiful restaurant with a couple of small dining rooms and terrace which are very elegantly decorated.  But there is no view.

Il Ritrovo - this is an interesting contrast to Donna Rosa, especially as they are a couple of doors down from each other.  It is home-styled cooking and equally delicious.  The atmosphere is more casual and has an outdoor terrace with a view.  This restaurant will send a bus to pick up patrons from their hotels and drop them back, though you do have to wait a bit (not too bad, though). Great value- dinner for two with appetizers, entrees, desserts and drinks is about 70-euros.