On the Krivan Mt., High Tatras, Slovakia
From the High Tatras there is easy access to many sights and towns in the surroundings, also thanks to the fast developing highway system in Slovakia.
Historical towns in the east like Levoca and Kezmarok are an one hour drive, and so is the castle of Spis.
And the High Tatras itself are compact and small; there are many different paths leading up and around them, and several lifts take you almost all the way up. Not everyone has to be a mountaneer to be able to hike there.
West of the High Tatras one reaches the Low Tatras in a bit over an hour, to visit the caves in the valley of Jasna or the picturesque village of Vlkolinec, which is on the cultural heritage list of UNESCO.
Down from the High Tatras is the somewhat greyish town of Poprad, where there is an extensive Aqua Parc, which is best visited off-season during weekdays as it can otherwise be quite crowded.