Bart
See the Alcazar and Ataranza in the Colonial District, as well as the small museum on Dominican history with all the Trujillo artifacts--I think it's on Calle de las Damas in the same neighborhood. Anywhere you walk in the Colonial District is packed with history. We spent 3 days in the area and didn't see everything. If you like to get into the feel of the Colonial zone, you might stay at the Hotel Palacio on Calle Duarte. It was once a presidential palace in the 1850s, and has alot of local flavor (OK, it's run by Germans and ain't too fancy, but it's pretty classy anyway). It's also one block from El Conde, the mall in the Colonial District, which is great for shopping and people watching.
If you really like museums, there is the Museum of the Dominican Man, too. It's a short taxi ride away but well worth the 2-3 hours to tour it in terms of understanding the country, people and their history.
Have fun! Susan