A great day trip is to Visegrad, a town on the Danube Bend, where there is an impressive castle.
It’s about a 30-50 minute hike up to the castle from the base. You can take trains from Budapest to Visegrad pretty regularly (note that the train station in Visegrad is on the opposite side of the river from the castle so you need to take a 5-minute ferry ride across once you arrive). There also are excellent ferries connecting Budapest to Visegrad,
although they take longer than the train.
Another possibility is a visit to Gödöllő, which is about 15 miles from the centre of Budapest. The main draw here is the Royal Mansion – the largest Baroque manor house in Hungary. Thee are many other lovely buildings and monuments to view as well. This is also accessible by train. Details at the Hungarian Railways website, www.mav.hu






