Been to the DR about six times so far. Where to go depends on what you're looking for.
The three main tourist/resort areas are Puerto Plata to the north including the funky town of Sosua, Punta Cana on the East coast and Juan Dolio/Boca Chica two beach towns east of the capitol Santo Domingo. Each has it's advantages. There are also a couple of resorts near Samana on the north coast but they're really isolated and the main attraction is whale watching
Punta Cana is the newest resort zone and probably has the nicest largest resorts with a great beach and all the amenities etc That said it's isolated so if you want more than lazing on the beach and considering the all inclusive bar a personal challenge then give it a miss.
The amber coast has a slew of resorts near Puerto Plata, many all inclusive and built around golf courses. Most are about 15-30 min cab ride into Puerto Plata which aside from some touristy craft markets and a small fort is just a seedy seaport. Some really good run down bars near the harbor, I recommend body armour. Day trips to Santiago to see a cigar factory, jungle tours or for the really adventurous Haiti are usually available from here.
Sousa just east is a tiny funky town with several budget hotels and one or two resorts I've stayed at Casa Marina twice, ok all inclusive, ok beach and one literally walks out the front door and you're downtown. The town is full of expats, bars, pick pockets, discos, and other attractions to separate you from your money. East of this is Cabarete with some of the best windsurfing in the region.
San Juan and Boca Chic are older beach resort towns with older and perhaps less impressive hotels and resorts. Main attraction here is easy access to the Capitol. The old part of Santo Domingo is well worth a trip for the history alone. Plenty of shopping, bars, restaurants etc here too. Also a whole street of quickie divorce lawyer offices.
One tip don't go during Easter week. Half the country is on holiday and the rest of the resort staff call in sick. The only one's working are the Haitian refugees and expats who run bars. The resort areas especially Puerto Plata and Sosua are also overrun with the upper class Dominicans from Santo Domingo. For the most part they're drunk, rude and get pissed when they're told thay can't carry they're pistolas in their speedos at the pool. Contrary to this average Dominican is polite and friendly even when they're mugging or conning you.
Another tip, the local beer Presidente is great. 8)
Plenty of good info and resort reviews here http://www.debbiesdominicantravel.com/