So I have 14 hours to spend in Budapest and almost no money. What are some cool free things to do there? Of course I want to walk around the city and see the architecture, but are there any free museums?
The thermae maiores under the overpass leading up to Árpád bridge in Buda is free to visit, a pretty under the radar sight but well worth the fifteen minutes of travel from downtown Budapest.
Also, there's two open air amphitheatres nearby, one at Aquincum and the other in Nagyszombati utca.
Anyways there are a couple of threads about Eastern Europe and Budapest up on this board right now, look them up and see if there's anything to your liking.
There's a phblic transport bus which departs every 10-15 minutes from the airport and will take you to the terminus of M3 metro, which you can use to get to downtown (get off at Deák Ferenc tér). It takes about 30-40 minutes tops.
Some museums are free if you're an EEA citizen under 26 years.
You can always try the art of riding the public transport without a valid ticket if you're looking for free, it is easier for locals, though.