Don't even consider getting a car. Parking in central Budapest is a nightmare. Just get a "travelcard" at the airport transportation desk located outside of baggage claim. They are good for 24/72 hour increments, and include all the metros. trams and busses.

http://www.bkk.hu/en/prices/

I'd seriously rethink the ING Holiday Inn pointsbreak promotion. The hotel is nice, but it's located way out in a light industrial area in the suburbs. Getting into town will require taking a suburban train to the metro hub in Buda. I'm guessing it's about 45+ minutes away. Budapest has lots of good inexpensive hotels in the city, and I would strongly recommend staying in town.