Within Baltimore itself, I highly recommend the Walters. It's an excellent art museum and (as of a few years ago) is free. In the same general vicinity, you can see Baltimore's version of the Washington Monument and the Pratt Free Library.

Other things to see in Baltimore are Fort McHenry, the American Visionary Art Museum (especially when they do the kinetic sculpture race), and the aquarium (which is excellent but pricy).

The most popular place amongst my admittedly nerdy friends in the nearby suburbs is the National Cryptological Museum.

Within a couple of hours driving, you can get to much of the rest of Maryland or to DC or to Delaware and parts of Pennsylvania and Virginia. I will second the suggestion of Annapolis and also mention that the historic part of Frederick has quite a lot of interesting places. Since the sesquicentennial of the Civil War is approaching, there will be even more than usual going on at the various Civil War related sites in the area. (About half the war was fought in Virginia. Given the number of reenactors, it often feels like it was fought weeks ago, not 150 years ago.)

Again, if you tell us more about what stuff you like, we can help you find things to do.