We stayed at Coco Point Lodge a couple years ago - nothing fancy in terms of accommodations but on a wonderful 2.5 mile stretch of beach.

Barbuda is a very "quiet Island" with miles and miles of beautiful beaches, only a few resorts and guest house, a few restaurants, a couple of beach bars (with limited hours) and a few points of interest. Go here if you truly want to "get away from it all". You can go all day and not encounter more than a handful of people.