Innsbruk, Austria
Innsbruck is known as one of the most outdoorsy towns on the planet with a reputation for easy access to extreme sports. So of course it's a prime location for rock climbing. It has fantastic amenities geared toward climbers, including the Kletterzentrum Climbing Facility (where the Austrian national team trains), the Alles Klettersteig climbing school, and several affordable hotels that cater to climbers. Sport climbing, multi-pitch, bouldering—whatever climbing you prefer, you'll find it around Innsbruck. Be sure to get an Innsbruck card to make use of free public transportation, among other perks.
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Kalymnos, Greece
Greece has phenomenal climbing both on the mainland and on many of its more than 200 islands. But if you don't have time to make multiple stops, stay on Kalymnos. You can fly there from Athens or take a ferry from Kos. The small island has more than 2,000 lead and top rope climbing routes along with several climbing clubs and guiding companies. First-time climbers can take a beginner class with Climb Kalymnos and experts can find world-class guides to show them the best spots.