I think there is a lot to be admired about Robert E Lee, but it doesn't change the fact that he chose to fight for Virginia over the Union. Let's also not forget that when the war ended Robert E Lee stopped fighting, swore allegiance to the Union and was also opposed to Civil War monuments.

“As regards the erection of such a monument as is contemplated, my conviction is, that however grateful it would be to the feelings of the South, the attempt in the present condition of the Country, would have the effect of retarding, instead of accelerating its accomplishment; of continuing, if not adding to, the difficulties under which the Southern people labour.” - Robert E Lee

http://www.pbs.org/newshour/updates/robert-e-lee-opposed-confederate-monuments/

Personally, though, I think monuments in places like Gettysburg and Antietem should stay. Not to venerate, but to commemorate the struggle on the grounds where they occurred. I find value in seeing monuments that are placed in the exact location where somebody stood at a critical point of battle or where a certain general might have been wounded or killed. I took a self-guided audio driving tour at Gettysburg 6 years ago and those monuments are valuable in imagining the battle as it unfolded.

Get rid of the rest though. If the monument doesn't mark a place of historic importance, its not serving any purpose, but to fan flames of hate intolerance on one side and oppression on the other.