The ride up Mt Mtatsminda on the city's funicular is spectacular, as are the views from the top – and there are a couple of great places to eat or drink, as well as dozens of funfair rides too. It's also several degrees cooler up here than in the city below, which can be very welcome in the heat of summer.
To ride the funicular you need a 2 GEL plastic card (sold at the ticket office) on which you then add credit for your rides (and any rides in Mtatsminda Park).