Visegrad

Located about 25 miles north of Budapest, Visegrad is a tiny castle town on the banks of the Danube River. It makes a nice day trip from Budapest, but is also worth a couple days in its own right, as it makes a great base for hiking and other adventure sports in the surrounding area. Visegrad was first mentioned in the history books more than 1,000 years ago and was a Roman stronghold in the time of Constantine the Great. The Turks destroyed most of the town in 1543, but it gradually rose again and regained town status in 2000. 
One of the most popular sites in Visegrad is the Royal Palace, originally built in the 14th century and reconstructed in a Renaissance style by King Matthias Corvinus in the 15th century. The palace felt into ruin after the Turkish occupation of Visegrad and eventually became completely buried. Excavations began in 1934 and today the reconstructed palace is open to the public and includes exhibits on its long history.
The Citadel, or Upper Castle, was built by King Bela IV in the 13th century to defend against the Mongols and is also open to the public. The Solomon Tower, which is part of the Lower Castle, also dates to the 13th century and today is home to exhibits of Gothic and Renaissance artifacts discovered in Visegrad. Climbing the tower offers great views of the surrounding area.

Practical Info

Visegrad is easily accessible from Budapest by bus, train and boat. Hydrofoils leave from Vigado ter in Pest and from Batthyany ter in Buda once a day between April and September and take about an hour. A cheaper (but less scenic) option is to take the train from the Nyugati train station to Nagymaros-Visegrad and then hop a five-minute ferry across the Danube to Visegrad. The train runs every hour and takes about 40-60 minutes. Finally, you might catch a bus from the Arpad hid bus station, which takes about 80 minutes, departing every 20-60 minutes.