When you do plan your trip, check out the events scheduled for the battlefields you will visit. There are often tours, lectures etc.
Appomatox is an interesting place to visit. When we were there last, there was a presentation about the battle from local inhabitants’ perspectives. It was really interesting.
If you’re going as late as December, Antietam Battlefield has an annual Memorial Illumination, when they light a luminaria for every soldier killed, wounded, or missing in this battle, the single worst day of the war. That’s over 23,000 lights on the battlefield. You take the tour by auto, but it’s still immensely moving.
This year it’s December 6th or 13th, I can’t tell from the Park Service website.
If you go, go in daylight to tour the field – it’s one of the most open and visible Civil War battlefields – then have an early dinner nearby, and return for the Illumination Tour. It’s really something to see.
I have been to most of the Civil War battlefields in the DC area and far and away, in my opinion, is Antietam.
It beats out Gettysburg because almost all the battlefield is much the same as it was in September 1862. It makes walking the area much more rewarding.
Also it was the more important battle. By July 1863, barring a catastrophic defeat of the Union army in Virginia (which Pickett’s charge was unlikely to provide), the South’s fate was largely sealed. But a victory by the North at Antietam (which a competant general should have pulled off) could have ended the war.
Just my $.02, YMMV.
Sandy: Also, Lincoln was ready to issue the Emancipation Proclaimation, but needed a Union victory, Antienam was that victory.
I’d also want to see Williamsburg, but it’s a trek from DC. 
I thought that he made a speech at Gettysburg too . . . hmmm, what was it called. 
Checked out Gettysburg on the way to DC this year and the kids loved it. The Cyclorama was an unexpected treat and we were able to get a private guided tour of the battlefield for only $60. I’ve been told the battlefield has been much improved lately. Still, I’d like to check out Antienam some day too.
Another Gettysburg point: if I were driving to DC and I wanted to visit Civil War sites, I’d consider hitting it on the way since Google Maps says it’s only 1 hour further (so you’d save an hour: if you were going to see it anyway you’d only spend an hour to get there, not an hour to get there from DC and another hour to get back to DC,) and you have to drive through less of the NYC/I-95 New Jersey area. But if I were from Boston, driving in NYC might be a relief 
Yep. 90 to 120 minutes drive depending on where you’re heading from in the area.