We stayed at The Harborside Inn, which is in the midst of things in Edgartown. It sits on the edge of a gorgeous residential neighborhood which is fun to wander and look at the beautiful homes and gardens. The Harborside is a very nice place, especially if you can reserve a balcony room with a full-on view of the harbor. The lodging we had was in one of three historic whaling captains' homes, which are very well-maintained and charming.
Our room was good-sized, with a relatively new bathroom. The ceiling fan and A/C kept it cool, plus its beautiful little private balcony provided extra space. We were extremely pleased with it, having read a negative review on TripAdvisor that the hotel was dated and rooms extremely small, which was NOT our experience.