Have flown into the D.R. many times in our Cessna Citation. Punta Cuna (on the east end of the island) has very nice 5 star resorts. The airport has good to excellent facilities. They are so many 5 star resorts on that end of the island I can't remember them all. The Haiti situation should not affect anything. Haiti is on the western end of the D.R. island. Don't know about the cheap part.
Santo Domingo the capital is a nice tourist stop. Lots of history. sites to see, but mostly the "business" center of the country. The InterContinental downtown is a nice hotel with a casino. "Old" Santa Domingo has the old spanish sites, etc.
I wouldn't go out of bounds of the resort complexes at night. There is crime. If you stay at one of the all-inclusive resort complexes, you won't need to go anywhere to relax, to swim, tennis, golf, eat, drink, etc.
I believe several months ago the government devalued their currency which makes it an an attractive bargain for the dollar. But the exodus out of the country by the residents to Puerto Rico has increased considerably in the past few months as this is truly a blighted country.
The airport is served at Punta Cuna by quite a few US and foreign carriers. Your local travel agent will probably have mucho info.