What are your parents' interests? That will have a huge bearing on what you should do.

If they are the type that would spend the entire day at museums and monuments, it might be better to head north (although Baltimore might be a nice compromise).

If they are the type that like to do things like see live music, go shopping, visit festivals, got to bars and meet people, etc., then you should be fine in DC since the shutdown won't affect private social activities. Going right across the river into Virginia will afford you similar facilities to National Parks and museums in the way of State Parks and museums, which are not shut down by the Federal Government. Old Town Alexandria in Virginia is a nice alternative to some of the landmarks in DC, and maybe more representative of the East Coast that DC is. Old Town Alexandria is also accessible by subway (Blue/Yellow Line).