Tbilisi's most interesting shopping is for Georgian-specific things: wine, handicrafts, antiques, and spices.
Wine: The wine shops on and around Erekle II Street in the old town stock a good range of Georgian natural and traditional wines, including small producers not available outside the country. Georgian wine makes an excellent (if fragile) souvenir — buy it on your last day.
Churchkhela and sweets: Churchkhela — walnut chains dipped in grape juice and dried into long cylindrical sweets — are sold everywhere. The best come from Kakheti and are recognisable by their size and the fact that the grape coating is quite thick. The market at Samgori sells them cheaply; tourist shops in the old town charge more.
Antiques and art: The Dry Bridge Market is the best place for Soviet antiques, old icons, paintings, and oddities. Prices are negotiable. The galleries around Shardeni Street and Gudiashvili Square sell contemporary Georgian art.
Spices: A bag of khmeli-suneli (the dried herb blend used in most Georgian cooking) and adjika paste from the Samgori market are cheap, pack flat, and transform your cooking at home.