Here are my suggestion...
If you want to truly enjoy the eastern section of the DR well, you should consider doing the following, though not all because you might not have time to do them all. But, there's always next time!
1) Stay in either Santo Domingo's Colonial Zone or Juan Dolio. The Colonial Zone is very historic and beautiful. It feels very much like Europe with a Dominican filter. Many small hotels here located inside buildings where important historical people once stayed at, example would be the Nicolas Nader Hotel ( I think that's the name) it's in the mansion of Nicolas de Ovando (the first governor of Santo Domingo Colony) and Columbus himself stayed a couple of times there. Who knows, you might just sleep in the same room such historic people slept in over 500 years ago? See the appeal of the Colonial Zone?!
Juan Dolio is great is you want a beautiful beach at your door step. There are lots of all-inclusives (what a surprise!
), but the Barcelo Hotel Chain also operates a small hotel there that is not all-inclusive. It's set back from the beach, but who cares when you can walk the 5 minutes of so under tropical soothing Palm trees and trade winds! The beaches in Juan Dolio are perfectly fine and beautiful with mature palm trees and clear waters, however, the beaches there are no match for what's found in Boca Chica, La Romana, or the Goddess of the All-Inclusives Punta Cana. Don't start to panic, the beach in Juan Dolio is still nicer than most beaches around the world. In addition, you will only be 45 minutes east of the Capital, 30 minutes east of the America's Airport, 15 minutes west from Sammy's birthplace (San Pedro), and there are some wonderful golf courses nearby (like Guavaberry) and lots of activities at the resorts. There are some local businesses in the area for you to patronize also.
EXCURSIONS
1. Isla Saona, if you have the chance of taking this tour, by all means take it! It's heaven on earth, and no this is not a cliche, it's true!! The most beautiful place on earth, hands down, well, Maybe Samana could give it a nice competition.
2. Scuba Diving at La Caleta Underwater Park, this is between the Airport and the Capital along Autopista Las Americas. There are some boats that were sunk in 1984 that have grown some nice corals on them. Alot of colorful fishes, very nice scuba place. If you like the underwater world, consider this!
3. Altos de Chavon, I know you said no sightseeing, but how can you be so close and not go! Instantly you would feel like if you left the DR and stepped into Italy! Aside from the beauty of the town, the views are so nice that if you forget your camera, no one will believe you back at home. There are also some cruises in an old Mississippi style river boat up the Chavon River. Very scenic river with high cliffs and coconut groves over hanging along the meandering river. Paradise at its finest!
4. Parque Nacional del Este, if you like birdwatching this is the place to go! So many birds of so many colors that it's unbelievable. It's a shame that Hippo wants to slaughter all of this, so go now before it's lost forever.
5. Punta Cana drive, if you decide to sleep in the America's Airport vicinity and head for PC the day after your arrival, you should consider driving to Punta Cana via Highway 4, instead of Las Americas. Highway 4 can be taken by turning left at the rotonda once you enter San Pedro. Follow that road all the way and it will become Highway 4. The road will take you to Hato Mayor, in the town of Hato Mayor (I don't really like this town, though it does have some charm) make sure to follow the Highway for El Seibo and not Sabana de la Mar. Between Hato Mayor and El Seibo you are going to witness some of the most peaceful and drop dead gorgoeaus Tropical countryside on the planet! Very sparsely populated area, but gorgeaus the full way. Once you reach El Seibo (nice town in my opinion, though not affluent) you should keep going towards Higuey. The ride is still very nice. As you approach Higuey you can't miss the highest belltower in the Hemisphere that belongs to the Cathedral of the Altagracia (the holiest spot in the country). The church is suppose to look like a pair of hands in prayer (took me a while to figure it out). The insider just makes you wonder how they built it, it's really impressive. The church looks best under sunlight, so if it's overcast, don't bother taking a picture from the outside because it looks like something from Transilvania or something. From there, follow the signs for Punta Cana. Lovely terrain, though it gets drier until you hit the coast. Once on the coast, enjoy some of the most idillic beaches anywhere.
There are other stuff to see and do in the area, but this is enough to satisfy your appetite for Dominicaness. Enjoy!