That's the only way to see a battlefield. Two of my great great grandfathers fought at Chickamauga, and we got very organized to take our two children on an extensive tour of the battlefield. I wrote the park historian (he is a great fellow, turns out he attended the same school in Maryland that one of my gg grandfathers graduated from -- small world!) and he provided a lot of information on the historical markers on the battlefield and an excellent topo map. We started in our ancestors' position before the battle began and basically followed their progress through the scene. Fortunately one was artillery and the other a scout, and both were in the thick of things.
And you're right, the only thing we needed the visitor center for was a Coke and a smile. We did stop to see the film, though, since we were there. It was pleasant, accurate, and not politically correct, the framework was the shades of two soldiers, blue and gray, looking back over the battlefield and trading reminiscences. Kinda neat and related to what really happened - it was the first battlefield park and quite a number of former combatants assisted in the effort. After reading a couple of the historical markers on the ground it became obvious to me that they were NOT written in the usual style - one involving the action of a gg grandfather just "read" like he had written it (he had a very distinctive writing style) so I wrote the historian and asked him if the participants had helped write the markers. He responded that yes, indeed, participants in key actions had been invited to "write their own markers" subject to approval by the committee.
Imagine what a bunch of PC revisionists would do with a bronze marker written by one of the hated Rebels . . . :-(
Chickamauga allows horses, and has not allowed the fields of that time to overgrow. So the very best way of all to see the area is a "battlefield ride" - on a horse who is steady enough to allow you to unroll a map on his/her back. I have been trying to talk my trainer into leading a field trip up there, combine a little history with some riding (if I can just figure out a way to work some JUMPS into the mix, I think I can sell her on the deal.)