i have used priceline in the past and got marriott and renaissance towers for a very reasonable price (under $100 per night)
you could try priceline.
if you are staying at a timeshare resort, check their website to see if anyone is renting out single nights that match your needs.
then there are places like brickel bay (perpendicular to the hyatt), talk of the town (near the rotary just beyond parliament), holiday inn, mvc eagle beach (incredibly basic), .......go over to the WHERE TO STAY category and do some poking around there.
Sunset Beach Studios is a great place but you will need a rental car. Paradera Park Apartments is in a local neighborhood over in Paradera and it is also a great place to stay--rental car needed there too.