Georgia has been making wine in clay vessels called qvevri for at least 8,000 years, and wine culture is embedded in Georgian identity in a way that is hard to overstate. Tbilisi has a thriving wine bar scene, centred on the old town and Erekle II Street, where you can taste both conventional Georgian wines and the amber (orange) wines that have attracted international attention.
The amber wine style — white grapes fermented with extended skin contact in qvevri buried underground — is unlike conventional white wine: tannic, complex, oxidative, with a deep amber colour. It can take some getting used to, but the best versions (Rkatsiteli and Mtsvane are the main grape varieties) are genuinely extraordinary. Look for wines from the Kakheti region, especially from producers like Pheasant's Tears, which has a wine bar in the old town and is a good starting point for tasting.