i am not sure what do you qualify as local cuisine. best restaurants in POP serve what i would call international dishes but they do have side orders of, say, tostones or yuka.
the best restaurants is the one in casa colonial but it is very expensive. other good places are, in no particular order:
las palmas on luis ginebra, their seafood soup is just great.
la tarrapa, close to the malecon has great pizzas
la parillada on the roundabout has a grat choice of grilled meats
stefy and nataly on the way to cofresi has fantastic pizzas and variety of italian dishes
sole mio in costambar, again good pizzas
taste on luis ginebra serves sushi at good prices and has great meat and fish dishes
kilometro zero, opposite taste has basic menu of fish and meat
su****o also known under some other name that escapes my memory now, close to tropical has sushi, of course and good tacos
but for more typical dominican food you can drop by dona gloria, one of the little houses on the malecon, she has nice burgers, chimis and so on.
further down the malecon, close to la sirena, there is a lady who sells empanadas from the balcony of her house, really nice! i am a big fan of empanadas
oh, i see that the system deleted the name of the last restaurant
small sushi, in other words