Budapest is connected directly to over 100 cities.
A complete list is on this Wikipedia page, at the bottom.
TRAIN / BUS
A train or a bus may be a viable option from neighbouring countries, and some other cities further afield. There are direct trains from cities like Zurich, Munich, Berlin, Dresden, Prague, Bratislava, Vienna, Kosice, Kiev, Cluj, Brasov, Bucharest, Belgrade, Zagreb.
Long distance bus routes connect Budapest with places like Stasbourg, Heidelberg, Rotterdam, Kraków, Oradea, Florence, Graz, etc.
For anything further than km, you’re really better off flying.
Driving may be a good option if at least 2 people come from the same area. You’ll need to buy motorway permits before entering the country. The shortest available period is 10 days and costs about 15€.