You can book an all inclusive package for not much more then airfare, then rent a room as you need it. It depends on how much experience you have in the Caribbean, and how comfortable you are with going somewhere with no place to stay and no food to eat in advance. The resorts are like home, the homes you book in the Caribbean, and the food you find, could be much different. Thinking the booking airfare, and then finding a place to stay, and food to eat when you arrive is for the advanced Caribbean travelers.
I have never been to the DR, but if it is anything like Cuba, then you really want to have a resort to go to if things do not work out. It is like paying $2-300 in guaranteed comfort insurance for the week. And you can eat and drink at the resort.