Gettysburg is also close, just up US-15 from Frederick.
Nothing wrong with Williamsburg (about a 4 hour drive) or NYC (another 4 to 5 hour drive, depending on traffic, or a 3+ hour train ride), except that they are far. If you are interested in other local (non-DC) history sites, Fort McHenry in Baltimore (http://www.nps.gov/fomc/index.htm) is worth a visit. There is also a museum to the Star Spangled Banner in Baltimore (http://www.flaghouse.org/). I have never been, but it looks neat.
I hope this help and happy to help more.
Closer to where you'll be (or along the way): Frederick is about 30 minutes away. The Monocacy battlefield nearby pales in comparison to Antietam and Gettysburg, but Frederick has an amazing Civil War medicine museum.
Not a Civil War site per se, but the Clara Barton House--with Civil War exhibits--is about 15 minutes away in Glen Echo. This is along the way if you're headed into DC.
IMHO There are three "Must Sees":
http://www.nps.gov/foth/index.htm (2-3 hrs)
http://www.nps.gov/gett/index.htm (FULL day)
http:///www.civilwarmed.org/ (2-3 hrs)
There are several other good sites
http://www.nps.gov/hafe/index.htm (half day)
http://www.nps.gov/ancm/index.htm (2-3 hrs)
http://www.nps.gov/mana/index.htm (2-3 hrs)
http://www.nps.gov/frsp/fredhist.htm (half day)
I agree with the suggestion of Fort McHenry