Night travel especially in the center of Budapest is relatively good. There is substitute for the M2 (78E) and M3 (50E and party 14E) underground lines and also for the tram No 4 and 6 (6E). “E” is standing for “Ejszakai” which means “night” by the way. These 3 run like every 15-20 minutes. Are you living further away? There are also substitutes for other bus and tram lines as well, but not as regular as these 3…check the website for more info. And look for the crowd around the stations being substituted…it will be easier to find the alternative (night) stations this way! 🙂