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...but in close reach by train, car or bus.
AUSTRIA
Donau Insel Fest in Vienna
Date for 2009: June 26-28
Website: http://www.donauinselfest.at/
CROATIA
Rabac Summer Festival
Date for 2009:
Website: http://www.rabacsummerfestival.com
CZECH REPUBLIC
Salsa Festival Prague
Date for 2009: June 5-7
Website: http://www.salsafestival.cz/
Rock For People in Novinky
Date for 2009: July 4-6
Website: http://www.rockforpeople.cz/
ROMANIA
Golden Stag Festival in Brasov
Date for 2009: ?
Website: http://www.cerbuldeaur.ro/
POLAND
Przystanek Woodstock
Date for 2009: July 31-August 2
Website: http://en.wosp.org.pl/woodstock/
It is very far away from Budapest, but this is the only summer festival I found in Poland.