Mtatsminda — "Holy Mountain" — rises above the city's western edge and is reached by a funicular from the foot of the hill near Rustaveli Avenue. At the top, a Soviet-era amusement park with a Ferris wheel and other rides sits beside a television tower. The views from the summit over the whole city are the main draw: on a clear day you can see the Greater Caucasus mountains to the north.
The funicular station is on Chonkadze Street, a short walk from Freedom Square. Rides run regularly throughout the day and into the evening. The park at the top is a little run-down but charming in a retro way; families come up in the evening and the Ferris wheel provides good aerial photographs of the city. The Panteon cemetery on the hillside, with its mix of Georgian literary and political figures, is worth a stop on the way down.