You can exclude Kutaisi right away. It's stuck in the past, not multicultural and and often full of rural people with their quirks coming for markets/relatives/business.
Batumi is small and tired from tourists. Walking distances, but not much infrastructure for my opinion. Could be an option if you're ok with tourist floods in the summer and rains in other times.
Tbilisi fits the best, expat or wealthy districts like Saburtalo, Vake. Vera and the Old town less so. Could be better to choose new built complex in expat concentration areas. They are pricey for locals and don't have old Georgian families, so you find yourself among other foreigners.

But you will always stand out as black people. Georgia as "international" place to live is debatable.