Veszprém makes a good base for the northern Lake Balaton region. The lakeshore is 15 minutes south by car. Closer at hand: Herend, 15 km west, is home to the porcelain factory established in 1826 and still producing some of Europe's finest hand-painted ceramics — the factory tour and museum are worth the short trip. Tihany, with its abbey perched on a peninsula in Lake Balaton, is about 25 km south.
For a longer outing, the Bakony Hills north of Veszprém are a lightly visited area of forests, limestone caves, and small villages, with walking trails through the Bakony-Balaton UNESCO Geopark.