I just checked out the list of people on our money that Rodgers01 linked.
I have no problem with recent non-politician choices on our currency, like Sacagawea and Susan B. Anthony (both on dollar coins). Furthermore, since I am in a generous mood, I will give passes to two head-scratch-inducing choices: Salmon P. Chase ($10,000 bill), who as the Secty of the Treasury was intimately involved with US money matters, and President William McKinley ($500 bill), who was "martyred" in office.
But Grover Cleveland? Really? What the hell made him worthy to be on our $1,000 bill?
(Oh, and for the purposes of the OP, yes, I think Andrew Jackson should be booted from the $20 bill. Historians claim he redefined the office of presidency, but I think his flaws (including the big political ones, not just his personal failings and orneriness) far outweigh his good points.