My recommendations would be Banana Beach or Villas at Banyan Bay. Both are condotels about 1 1/2 miles south of town. Both have pools, are on one of the best beaches on the island and have lovely suites -- Banyan Bay has two bedroom units with jacuzzis, Banana Beach has one-bedroom units. Banana Beach in the summer would be well under your budget limit, Banyan Bay about at it.
Banana Beach does not serve breakfast, but you can get a good moderately priced breakfast next door at Tropica or elsewhere within walking distance.
Both Inn at Robert's Grove and Chaa Creek are top notch -- you can't go wrong at those places.
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