From City Hotel Pilvax to the Eötvös University Lágymányos campus (ELTE TTK):

Take the blue metro line M3 from "Ferenciek tere" station to "Ferenc körút" station (2 stops). Costs one ticket (140 Ft, 0.5 Euro). Go up to the surface and take a yellow tram no. 4 or 6 You have to choose the Buda/Danube direction ("Boráros tér felé"). Costs yet another ticket. Immediately after crossing the Danube ("Duna") trough the Petofi Bridge (Petőfi Hid) you have to take off. The stop is called "Petőfi Híd Budai Hídfő". On your left (south) you can see a new building with an observatory on the top. You have to go there through the park.