Before getting there, I had no idea of this, but Budapest sits on top of a massive network of caves that are open to the public. So yes, you can actually go spelunking under Budapest, and it's pretty easy too. Most hostels let you make a booking to go with a group and guide, and it's pretty cheap (equivalent to about €20 from what I remember). Obviously, Blake and I did this.
We met a group of backpackers later that day at a determined location in the city center, and once everyone was there, we boarded a bus for the cave entrance on the city outskirts. I was feeling a an odd mix of tired and excited at this time. Excited because I was about to go spelunking for the first time in my life, but tired since I now had about two weeks of compounded sleep deprivation and was currently running on a caffeine deficit. But anyway, just as I was mid-yawn, Blake struck up a conversation with two Irish girls on the bus, Maud and Hannah, and soon we were all chatting like we’d been friends for years (foreshadowing!!!). The tiredness went away.
Then we arrived. I still wasn’t quite sure what to expect. Maybe they were something similar to the open, well maintained salt mines of Krakow, or maybe they were something that more closely resembled a bear’s dwelling. I had no idea, but first thing first, I made sure to get a coffee before we started (addiction). Then they handed up our equipment which consisted of a full-body jump suit and a hardhat with a headlamp. Ok, this seems legit now. We entered… and it blew my mind. Before me now stood massive network of vast caverns and narrow crawl passages, which was in no way smooth or polished. They were rugged, untamed, wild caves, born out of clay and rock. I going to get down and dirty and when they had up shut off our headlamps, everything became entirely pitch black. It was just us and the cold, dark underbelly of earth. And it was amazing!
Wards of warning: If you are not nimble and tremendously lack flexibility (like me), Some of the crawl spaces will be difficult to get through, and sharp rocks will poke you in unfortunate places. That said, still totally worth it!