Over the past few years, Tbilisi, Georgia, has become a red-hot travel destination. The far-flung city boasts a bevy of ancient activities, like its tried-and-true sulfur baths and the centuries-old tradition of drinking kvevri-fermented wine. But it’s not all Old World in Tbilisi: The city’s modern attractions include the techno club Bassiani—located in the maws of a drained swimming pool—while tourists and locals swear by dinner at the raved-about hotel, Rooms.