Veszprém is located north to the Lake Balaton, 120 km from Budapest (see map).
If you arrive by airplane at Liszt Ferenc Airport, Budapest then you can take either train or bus from Budapest to Veszprém. Both stations can be easily accessed by public transportation. Of course you can take taxi or the Airport Shuttle in Budapest, as well. The local bus no. 200E departs from between Terminals 2A and 2B, its final destination is the terminal station of Metro 3, called Kőbánya-Kispest (see bus schedule). The intercity Bus Station is located at Népliget metro station. It is the fourth station on Metro 3 (see Metro schedule and Metro map). If you choose train, you have to go to metro station Deák tér, there change to Metro 2, and take off at the terminal station Déli pályaudvar (railway station). Alternatively, you can go to metro station Kálvin tér, there change to Metro 4, and take off at the terminal station Kelenföld (railway station). Trains depart from Déli railway station to Veszprém stop at Kelenföld railway station.
Uppdate: Due to the reconstruction of metro line M3, metro service on line M3 is replaced by buses on the weekends.
An alternative option from the Airport to Kelenföld railway station: take bus no. 100E from the airport to Kálvin tér (this bus has a special fare of 900 HUF), there switch to Metro 4 in the direction to the terminal station Kelenföld.
You can travel by buses, trams or metro in Budapest only with pre-purchased ticket that you validate when starting your trip. Its price is 350 HUF. Keep your ticket for the duration of your travel, controllers may ask you to show it any time.
Train: See the schedule of trains from Budapest to Veszprém. It is recommend to select only direct trains (without any change).
Bus: See the schedule of buses from Budapest to Veszprém. It is recommend to select only direct buses (without any change). (Sorry, this page works only in Hungarian recently. At the selection of the journey "Honnan?" means "from", and "Hova?" means "to". Also, you have to select the date of travel.)
If you arrive to Hungary by train through Győr, it is easier to take off from the train in Győr and travel to Veszprém by bus. See the schedule of buses from Győr to Veszprém. The train station and bus station are located next to each other in Győr (see map).