Will have a day to kill in Budapest and about three in Prague. Any suggestions besides going on an absinthe binge?
If you rent a car on the cheap for a day, drive SW out of Prague for an hour and go town hopping. The area is as pretty as Bavaria but a lot cheaper, equally quaint (and less touristy) and each town has a restaurant/pub or two with great local fare. When the locals figure out you are from the states, they'll be very friendly and inquisitive.
Driving between the towns is a blast. Narrow 1.5 lane roads with a white line on each side (no center line), very smooth and well kept and they follow the contours of the land so it's like being on a go cart path. I picked up my car on a Euro Delivery program last fall and enjoyed the drive there even more than the autobahn.