Santo Domingo doesn't have any beaches but Hotel Mercure Comercial Sto Domingo is in the Colonial City and is probably in your price range. Check this site.
Hotels Boca Chica – Boca Chica Countryside-, City- and Vacationhotels – Boca Chica Hotels with best price guarantee Chica&IsWCTSearch=&inMonth=&inDay=&outMonth=&outDa y=&adults=&price=
or
Hotels Santo Domingo – Santo Domingo Countryside-, City- and Vacationhotels – Santo Domingo Hotels with best price guarantee Domingo&IsWCTSearch=&inMonth=&inDay=&outMonth=&out Day=&adults=&price=