I walked the McDowell battlefield again a month ago. It's a better trip when there's no foliage. You can walk it from the Confederate perspective, pulling off of Rt. 250 before you get to the village, or the Yankee perspective, walking up to Sitlington's Hill from the village. (If you have two vehicles, park one in the valley, and walk all the way through, starting at the Rt. 250 pull off.) There is a small museum in the village.
In Richmond - The (former) Museum of the Confederacy is nice, but is headed downhill fast. It has merged with the politically correct Tredegar museum, changed its name (the word "Confederacy" was banned), and the mission is to tell its story from three perspectives. The White House of the Confederacy is right next to The (former) Museum of the Confederacy.
Also in Richmond - Hollywood Cemetery is beautiful. If you go, read about it first, figure out what you want to see, & either download a map (so you find what you're looking for), or visit when it's open (so you can ask for assistance & a map).
North of Richmond - the Wilderness, Spottsylvania Courthouse, Chancellorsville, & Fredericksburg are all close together. Chancellorsville & Fredericksburg have visitors' centers.
Petersburg is a big battlefield, with a lot of stations (you drive from one to another). On my last trip, a grossly overweight ranger was giving a talk to us, which quickly started to focus on the PC angle ("how would you feel if you were a slave?") was the last thing I heard her say before I took my exit. (I've been told there is a federal requirement that National Battlefield parks are required to cram that stuff down our throats, thanks to the not so Honorable Jessee Jackson, Jr. & others, maybe that's an urban legend.) The rest of my tour was great. When I got to the station that had the crater, there was only one other tourist, and the ranger was a good ole boy from Highland County (where the Village of McDowell is).
Drewey's Bluff (between Richmond & Petersburg) is a pretty spot, but it's not big & doesn't have a visitors' center.
There are the Manassas battlefields, Appomattox (The Museum of the Confederacy has a branch there, I haven't seen it), if you go to Gettysburg via I-81, both Harpers Ferry and Sharpsburg are close by.
If you hit Gettysburg - make sure you walk the charge route. Park near the Virginia monument on Seminary Ridge, there are two different paths cut through the fields, walk to Cemetery Ridge on one, walk back on the other. (Spray tick repellant on your feet & legs first!)