I'm planning my first international trip out of the U.S. this fall to Budapest, Hungary. I'm visiting a very good friend who will be studying abroad.
What are some things to see in Budapest?
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Budapest is known for its thermal springs, as they're the largest in Europe, so you should try one of the many baths, such as the Gellert (very central location, but a bit touristy) or the wonderful Szechenyi bath.
The market hall is great for some local food, but also to buy souvenirs.
The synagogue has some interesting and moving stories to tell.
The Buda castle is also pretty impressive and you have a great view over the city and the river Danube, especially during dusk, when the Chain Bridge is illuminated.
The Houses of Parliament are huge and very interesting if you're into architecture.
Relax and have a drink and some cake in the "Central" café, which is a very nice Viennese style coffee house (Budapest was under Austrian rule for quite some time, so there's lots of influence throughout the city)
Enjoy your trip!
Ruin bars are worth a look, and not just for a wild night out. They are night clubs but possibly not like you're used to. They are based in old derelict buildings houses, factories and office buildings that have been converted into clubs with makeshift furniture and sculptures from what ever was left lying around; cars cut in half and bath tubs as seats.
Szimpla is a rather big one that I visited in 2010, but apparently there are loads you just need to ask a local for directions.