Visegrad is not a nightlife destination. The town essentially shuts down after the day-trippers leave, and the options for a drink or a coffee in the evening are limited to a handful of places along the main road and near the riverfront. Most close early.
In summer, the outdoor terraces of the riverside restaurants double as places to sit with a beer and watch the Danube in the late afternoon. The pace is slow and the setting is pleasant. Beyond that, if you are staying overnight and want more animated evenings, Szentendre — with a lively cafe and bar scene — is the better base along the Danube Bend.