Upvote:2
The SUP (Stand Up Paddleboarding) website SUPTrotters has many examples of places in Georgia you can do stand up paddleboarding.
However, the strength, ferocity of rivers, cascades etc, would be worth investigating before launching an expedition on any type of river, anywhere. It may be worth using SUPTrotters to contact other users in Georgia as guides or for further advice or information.
Upvote:3
The best place near Tbilisi to paddle with your paddle board is Gldani-Nadzaladevi the Tbilisi reservoir.
The second best place near Tbilisi to do some Stand Up Paddle is Pshavis Aragvi River but be careful because water can be rough in most seasons.
The third best place to do some paddle board near Tbilisi is definitely Zhinvali Lake. That is fantastic all year round but in winter you need some protection from cold.
You'll be able to get paddle boards and kayaks to rent almost everywhere. There are a lot of websites that share list of good spots worldwide where to practice SUP safely. One that I remember about stand up paddle is paddlesurf, but there are really so many and all specialized on regional spots.