There is a penny press machine at Bubba Gump's restaurant in City Walk. There are too many to list in both parks and the parking structure. I use PennyCollector.com to look up the machines, since I have started bringing home several repeats.
I don't know if they fit your description of "cheap," but I like to start out a trip by getting a fun new lanyard. It's useful AND it's a souvenir. Win-win! I also get a coffee mug each trip - also possibly not "cheap," but not super spendy, either!