Spent a week on AC in January. Stayed at Brianna's Beach House - run by Searious Adventures. Complete 2 bedroom house with full kitchen. No pool, but a million dollar view from the front porch - oceanfront! South of the cut, a 10 minute walk to town, quiet and wonderful.....wouldn't have it any other way! Should be in your budget range at that time of year. The Tides Hotel is 2 doors down the beach and they have a pool - perhaps you could make arrangements with them....they also have a thatch covered bar where you can soak up a few Belicans and the Trade Winds (say Hi! to bartender Butch!)