There are some basic, but reasonable, studio / 1 bed apartments on Sanchez in Zona Colonial which rent for US$450 per month. The Colonial Zone is probably the safest part of Santo Domingo and has a lot of good amenities within walking distance - we're getting a Supermercado Nacional on the Conde this summer as well. The apartments I'm talking about are in the three-storey block on the corner of Mercedes and Sanchez, above where the Studio Bar used to be (which has now closed down).
Don't expect to get anything with a pool or sea views in the Colonial Zone for less than US$800 per month, that's pretty much the minimum now. Prices are rising quite steeply here as there are evidently 5 times more tourists this year than last year.