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Hungary
Check out Sopron (on the Austrian border), Lake Velence rather than ueber-touristy lake Balaton, Gyor, Szentendre (could be done as a daytrip from Budapest, though we did it the other way around) or Szeged (near the borders with Serbia and Romania - I wouldn`t go out of my way for it, if I recall correctly there`s busses to Arad, which would be cheaper than taking a train across the border).

Budapest


budapestindex.com
 
Places to Stay

Backpack Guest House - http://www.backpackbudapest.hu/

The Bohemian codes are still alive and well in this hostel. The staff as well as the highly-decorated rooms are warm and friendly. The 10-bed room I stayed in, called the "Bob Marley Room," is decked out in green, red and yellow and completed with a large mural of Bob Marley. I'm not joking when I say that they have the best bathroom in Eastern Europe. Bring a pen when you go so you can sign their "bathroom guestbook." The quality and comfort of the Backpack Guest House makes up for the long distance from the center of town. (it's located in Buda).

Hooray for Bori&Attila!
 
Haller Camping

A short ride on the metro from the city centre. Surprisingly few people staying here considering the number of tourists in Budapest.

Budgeting

Budapest isn't super cheap anymore. I spend at least $30/day there (but more like $40 usually).
 
I went there the first time in 1995 I think, and remember we everything cost twice as much as anywhere else in Hungary - it was still cheaper than western Europe, but I wouldn't have called it super cheap even then.
    
Things to Do
 
I really really liked Budapest.  It was just a mellow, nice beautiful place to hang out.
 
I liked Budapest much more than I liked Prague. Specifically, I liked the food and architecture better. It seemed more like a Grand Old Dame.

The tour of the Opera house is neat.

Take the metro/train to Szentendre which is an art town and catch a ferry ride back to Budapest on the Danube.  The ferry provides a nice venue for picture taking.

The trains through Budapest are excessively slow. My recollection was that it took about 18 hours. That includes the 4 hour stop at the border in the middle of the night while they were hassling people.
 
My biggest regret about Budapest was not going to the public bath in the park up by heroes square. They were renovating the building and were almost done, and it was beautiful. we just didn't get it together.  

Places to Eat

Special restaurant mention goes to Bagolyvar. Really Fantastic Food. it's pricier than what's usual in Budapest, but really just amazing, you'll need a reservation but they all speak English.  You can reserve on line on their website - bagolyvar.com.  They also run cooking classes that look like fun.

Day Trips

 
On the train from Budapest to Bucharest we met a couple from Bucharest who had been on their Honeymoon in Eger, which is Hungarian wine country. I've heard it's nice but as I didn't get there, I can't make a personal recommendation.

From Budapest it's 6-8 hours to Belgrade by train, then another 8 hours to Bar. Take the sleeper.  Waking up, brushing your teeth while seeing the Montengrin coast is one of the most enjoyable moments I've ever had.
 
There's other great places in northwest Hungary - Sopron, Györ, Lake Velence and Szentendre.  It is nice to see Vienna and Budapest right after one another.
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