Night time in Rike Park
Gold, gold, gold
Head for the National Museum on Rustaveli Street and get your fill of Georgian gold. The Treasury display starts with 'temple spirals' made in the third millennium bc - rams' horns inspired Georgian metalworkers right from the start (and you can buy real drinking horns today, just up Rustaveli towards the Rustaveli Square metro) - and continues with gold-covered medieval icons. If you're fed up with gold, you can head upstairs for a sobering exhibition on the Soviet occupation.
Try some craft beer
Wine and chacha may be more popular, but there are some good beers in Georgia. If you want to explore craft beer, take a turn up Lado Asatiani Street to find the Black Dog bar, serving craft beer and flavoured chachas backed up by a burger and burrito menu. On your way back, visit Naturale beer shop to buy a litre of take-home craft beer from the pump. Their rye beer is particularly good.
Visit one of the sulphur baths in the little gorge east of the Old Town. The little brick domes are the giveaway sign of old hammams - you can reserve a room for you and your friends or brave the public baths (don't bother to take a bathing suit, birthday suits are de rigueur here). Get a massage if you're feeling masochistic or brave.
All the fun of the fair
Take the funicular railway up to Mtatsminda funfair for one of the best views of Tbilisi from the Big Wheel. You'll also get a close up view of the TV tower, which always reminds me of a piece of space junk. Lots of stalls sell food, drink, and souvenirs - including delightful 'magic trees' made of wire and semi-precious stones.
Into hiking? There's a 'tourist track' which runs all the way from Narikala fortress to Mtatsminda on good tracks with paved steps. Great fun, but don't disturb the lovebirds communing on the park benches!
Holy, holy, holy
Explore Tbilisi's old churches. Mtekhi church on its rocky crag over the river has been rebuilt a few times since it was founded, but it's still atmospheric, and priests sometimes hold healing ceremonies in the little park beside it. The two Betlemi churches in the old town have modern but interesting frescoes, as well as a community of cats who hang out there, while the Anciscati basilica is dim and lovely, and popular for weddings.