The most interesting part of Santo Domingo is the Colonial Zone. It's also the most touristy, you'll need to beat the "tour guides" and t-shirt vendors off with a stick but the sights are worth the trouble. On one of my first trips there I wandered off El Conde (the main drag in the Colonial Zone) and happened upon a restaurant that has become my favorite.
El Meson de Lu is a a family operation. Luis, the owner, is usually there in the evenings. His wife tends bar, and his daughters run your drinks to you. When I first started coming to the restaurant they kept cartoons playing loudly on the TV to entertain the youngest daughter; thankfully (I guess) she has moved on to pop music shows.
There are a number of constant items on the menu. You can always get a great piece of grouper, fried or grilled, and there are garlic beef dishes. The rice and beans are a small miracle. The type of beans changes, but the wonderful creaminess doesn't. The amount of pork added to the beans is always just right. Last night I ate some fantastic goat, a special listed on the chalkboard. It had been braised and stewed, and it took me a long time to clear my plate. I find that when I've got really good food in front of me I naturally eat very slowly- a big deal for me, I tend to eat way too fast.
If you're in Santo Domingo, check this place out. The menu is in Spanish only. Luis speaks English well, but his wife and kids don't. I wouldn't worry; they are friendly and ordering has never posed a problem for me. The Mrs. can come off a bit dour, so don't read it as though she's inconvenienced by you.
Diagonally across the street is Meson De Bari, another good restaurant. It's not hard to eat well in this town.
Meson de Lu (sometimes you'll see it called Meson de Luis)
Calle Hostos #201