Budapest is very well connected to the major airports of Europe: there are plenty of low cost airlines including Wizzair , Easyjet, Germanwings . See also the national Hungarian Airlines Malev , which sometimes competes with the low cost ones in price but has higher standards.
We recommend to use the minibus shuttle service. It operates between the airport and the city center and the return ticket costs 4990 HUF = 18 €. 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 200 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 (320 HUF ~ 1.2 € each) in advance).
If you are arriving by train then you can take any official taxi around the stations (with a taxi sign on the top), but we advise to use public transportation as it is quite simple.
If you are arriving to the East Railway Station (Keleti pu.) you have to take bus number 7 (red is faster) and get off at Gellért square (one single ticket, 320 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, 320 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, 320 HUF ~ 1.2 € each).
We recommend to use the minibus shuttle service. It operates between the airport and the city center and the return ticket costs 4990 HUF = 18 €. At the airport you have to tell the name of the Hotel: Peregrinus (sometimes also the address 1056 Budapest, V. Szerb utca 3.)
If you intend to use public transport you have to take bus number 200 to the metro's end station Kőbánya-Kispest. There you can switch to the blue line of the metro until Kálvin tér. From there you can walk to the Hotel, see the map on the Hotel's webpage (You have to buy two single tickets (320 HUF ~ 1.2 € each) in advance).
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).