Punta Cana does have some of the best beaches in the DR if not the entire Caribbean, but you will mostly find all-inclusives there. Also, it is an isolated resort area and your interaction with Dominicans is going to be very limited.
On the north coast you have a couple of options. Both Costambar/Cofresi and Cabarete are nice areas where you will be able to stay at small non-inclusive hotels and greatly interact with tourists and locals. The same goes for Samana peninsula. Samana is my favorite. There are no slots here, rather utterly majestic natural beauty with green hills and crystal clear beaches. Two small resort "towns" to consider in Samana are Las Terrenas and Las Galeras. Small hotels are the norm in both places, but I prefer Las Galeras. Personally, I have visited (but not stayed) Villa Serena and Club Bonito in Las Galeras (both have websites - www.villaserena.com and www.club-bonito.com). In order to get to Samana you will want to fly into Puerto Plata and take the 3-hour Caribe Tours bus to Samana. The buses are first class [and inexpensive] all the way. You can also check out more information on Cabarete at www.hispaniola.com. For reviews of hotels, see link below. Hope this helps.
Regards,
Natasha