Because of the unique environmental conditions that created the many thermal waters and the cavernous Buda hills, Budapest is the capital not only of Hungary, but of spelunking. This oft overlooked hobby is actually a ton of fun, and is enjoyed by hundreds of thousands of aficionados across the world; it is the sport of going into caves and crawling around in them, exploring the life down there. It is part hiking, part boulder climbing, part extreme sports, and is a lot of fun. Budapest has many kinds of spelunking; form the very extreme to the mildest forms that can be done by a 3 year old (not to mention a 73 year old). Below is a list of some of the most awesome caves to go exploring in and around Budapest.
This natural limestone cave is a world of dripping water and underground statues that are incredible to behold. One of the easiest places to explore, this is a family friendly cave, with many small rooms and famous sites to see, including named natural statues, cool stairs and strange rock formations, but relatively close to the surface. This can be found in Buda in the 12th district, close to Kolossy tér.
More info here: http://www.dunaipoly.hu/hu/bemutatohelyek/szemlo-hegyi-barlang
The cave at Pálvölgy was also caused by the aquifers feeding off of the Danube, and is also a very family friendly affair. The cave itself is 29 kilometres deep, but only around 500 metres are available to laypeople, as this climb is safe and can be done with absolutely anyone, but more complex spelunking is done here as well, for the true fans.
More info here: http://www.dunaipoly.hu/en/bemutatohelyek/pal-volgyi-barlang
Located in the same place as the Pálvölgyi cave system, this was created by the same conditions, but is the more obscure cave of the two. Only guided tours are available of this particular cave, and it is a 2.5-3 hour tour. The rest of the cave is not available only to expert climbers, and is quite dangerous to the public. The safe tour can only be done by those in good physical shape.
The cave in Sátorkőpuszta is only open certain days of the year, and is closed for the winter months. During the summer, the cave is only 13 celsius, and those who wish to explore the cave must be dressed warm. This cave is one of the more difficult ones, and will take around 2 hours to go around in. The cave is unusually damp, so do not wear inside shoes, wear boots or wellingtons if you decide to embark on this journey.