Eden. No seriously, Eden.
You simply cannot beat Villa Degli Dei. Yes, the staff is exceptional, the room is very nice, and the price is laughably affordable, but the view. Oh the sweet Nocelle view. The Villa's are in Nocelle, a village situated 600 meters above Positano and offer once-in-a-lifetime views. Seriously, you will think god will come knocking at your door. Plus, the restaurant nearby, Croce, is one of the best in the area. Bear in mind that if you want to stay in Positano, this hotel is at the top of the mountain, so you will be forced to rely on the hourly bus, but it is very cheap and the view from the bus during your 20 minute ride down the mountain is a gift.
Pros: View. Quiet.