The last sentence of Susannes posting is thrue in any case, but the other points i do not agree.
I would suggest the big Cities, like Santiago, Puerto Plata, La Vega or the Capital St. Domingo. Puerto Plata for exemple is a natural grown city since almost 500 years. It dont belongs to the tourist industry with one of the oldest harbour in the "New World".
If you dont want to meet other tourists you dont have, because the percentage of tourist is much smaller than in little places like Susanne say.
And there you can stay in a little dominican Hotel or apartment and have a crowdy surrounding of local people/Dominicans. And even local restaurants/food (Comedores etc.)local nightlive, bars, dicos a.s.o..
Just the state how I would do it.......
Good luck & nice vacation!
cu/charlyloco