Originally Posted by
beltway
I agree with EmailKid that riding the old subway rolling stock is interesting.
I think the reference was to metro line 1 (the "underground" if you translate the Hungarian literally) rather than to the bog-standard metro line 3 which runs to Kőbánya-Kispest.
For anyone thinking of taking this way to/from the airport (which is generally perfectly do-able if you avoid rush hours), the metro line 3 is closed at weekends, until a date to be determined, for engineering work. This means getting a replacement bus along the whole length of the line, which I wouldn't particularly recommend.