To the best of my knowledge there are no AIs in Santo Domingo. There are hotels where you can pay extra to have meals included. If you are making reference to a hotel with meals, drinks, and entertainment (shows, movies, bowling, etc.) for one price you won't find any in SD.
Santo Domingo is not a city where you would want to stay on the hotel grounds all day. There are just too, too many other things to do.
As previously mentioned, Boca Chica would be the closest.