Take a train from Budapest Nyugati railway station to Nagymaros–Visegrád (cca. 40-60 minutes, runs every 60 minutes; the station will be on the opposite side of the river so you need to take a 5-minute ferry ride  across; ferries are scheduled to train arrivals), or take a direct bus at Budapest, Árpád híd bus station to Visegrád (cca. 80 minutes, runs every 20-60 minutes). A more expensive (but much more picturesque) way to get to Visegrád is an excursion boat and a hydrofoil service run by Mahart  (both daily once, only between April and late September).
A fortification system constructed in the 1240-50s near the former fortification destroyed during the Mongol invasion. The castle is open to the public for visit.
The Lower Castle is the part of the fortification system that used to connect the Upper Castle with the Danube. In its centre rises the Solomon Tower, a large, hexagonal residential tower dating from the 13th century. It is very visible when arriving to Visegrád on Route 11.
Partially rebuilt in Renaissance style (accessible to people with physical disabilities), a medieval residential tower and an impressive citadel, which is about 30-50 minute hike up from the base. The reconstructed royal palace building is open to the public, and hosts exhibitions on the history of the royal residence and reconstructed historical interiors.
The ruins of this Roman Empire military camp can be seen outside Visegrád, to the north, on a hill overlooking river Danube.
Toboggan runs near Visegrád, they have two parallel runs, one operates throughout the year, the other one is summer-only. 
Pillangós ház  cosy double rooms for HUF 13.000. It has wireless internet in the rooms and there is a small kitchen and lounge available for use. Lovely esoteric woman in charge.