What to know in advance
The square and the streets around it are busy during the day and into the evening, so a free space is not guaranteed.
Central parking is often paid or time-limited — always read the signs before leaving the car.
Alternatives
Parking on the streets towards Old Tbilisi can be more available, but you will then walk uphill to the square.
If you plan to drive, it is often better to leave the car outside the core and cover the last stretch by metro.
Practical tip
For a short visit, the metro or a taxi that drops you at the square is the least fuss.
If you do drive in, expect livelier traffic around the square in the evening.