If only the mighty walls of Castle of Veszprem could talk! But seeing they can't, check if tours are available to hear a couple of its stories instead.
You're spoiled for sightseeing choice in Veszprem. Castle of Veszprem is a great place to begin here, but there are plenty of other fine places to visit. Veszprém Zoo, Veszprem Arena, and St. Stephen Church are not far from the fortified complex and and will cap off your day nicely.