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).
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.