Oh, hmm. I feel like I've been to a lot, but the Lincoln home is the big one coming to mind right now. I know I've been to several ghost towns in California (cannot for the life of me remember which one) and Scotty's Castle in Death Valley. We went to Mammoth Cave last year, lots of local history there.
There was a Lincoln-Douglas debate in the city park, but I don't really think that counts. And I've been to the U505 exhibit at the Chicago Museum of Science and Industry several times...it still smells like a real ship!