How long are you staying around Petersburg? There are several sites in and around Richmond (which is only 20 min. or so away) that might interest you.
It really all depends on what you want to see (i.e. battlefields, museums). Once you get a final list share it with us. We'll tell ya straight.
"War is sorrowful, but there is one thing infinitely more horrible than the worst horrors of war, and that is the feeling that nothing is worth fighting for..."
-- Harper's Weekly, December 31, 1864