Yes there is.
They have one located in the center of Puerto Plata, next to Bournigal Hospital. It's called
Movie Maxter. I recomend this one, because they have a very good movie inventory, Old & New Releases. Very good service, Air conditioned location, secure parking space. and english speaking employees, only rent DVD's, Prices go from 50.00 pesos a regular movie to 60.00 pesos a new release, Rent one get two on tursday's, open everyday, from 10:00am to 10:00pm.
There's also two new stores in town, but
Movie Maxter has better prices and the most updated inventory, also the best location.
Their Phone # is (809) 261-5746
Maybe you want to check their Website too.
www.moviemaxter.com