Budapest-Ferihegy is a very nice airport (I was earlier this year). It is very spacious and extremely clean. It is all now concentrated in two terminals Ferihegy 2 and 2B. On the later you can access an outdoor viewing terrace (you must pay a small fee and pass a metal detector) where you have a good view of the tarmac. Also taxing aircraft and the runways far behind.
Exiting the airport you should not miss if you can the Malev Museum. It has several old aircraft including Tupolevs 124, 154, etc.