Budapest is very well connected to the major airports of Europe: there are plenty of low cost airlines including Wizzair , Easyjet, Germanwings .
We recommend to use the minibus shuttle service. It operates between the airport and the city center and the return ticket costs 5500 HUF = 19 €. At the airport you have to tell the name of the Hotel: Gellért (sometimes also the address 1111 Budapest, Szent Gellért tér 1.)
If you intend to use public transport you have to take bus number 200E to the metro's end station Kőbánya-Kispest. There you can switch to the blue line of the metro until Kálvin tér, where you have to take tram number 47 or 49 to Gellért square (2nd stop) where the Hotel is situated. (You have to buy three single tickets (350 HUF ~ 1.2 € each) in advance).
If you are arriving to the East Railway Station (Keleti pu.) you have to take bus number 7,173 and get off at Gellért square (one single ticket, 350 HUF ~ 1.2 €).
If you are arriving to the South Railway Station (Déli pu.) you have to take tram 18 and get off at Gellért square (one single ticket, 350 HUF ~ 1.2 €).
If you are arriving to the West Railway Station (Nyugati pu.) you have to take the metro to Kálvin square (tér), where you have to take tram number 47 or 49 to Gellért square (two single tickets, 350 HUF ~ 1.2 € each).
We recommend to walk following the route marked on the map (it takes about 15-20 minutes). If you want to use public transport you have to take tram number 47 or 49 to Móricz Zsigmond körtér, then change to tram number 6 for two stops, take off at the Buda side of the Petőfi bridge, from where you can again walk to the Physics Building (Eszaki Tomb).