It’s possible you’ve already seen some photographs of Tbilisi on my website as I was spending there some days last summer while trekking through Georgia. (See a detailed day-by-day travel journal for Georgia)
I really liked Tbilisi last summer but I read it’s especially beautiful in May. Two reasons two make Tbilisi my start point for my latest journey to Eastern Turkey. It’s a bit of hassle to reach Turkey from Tbilisi as it involves train, taxi and several buses but it was really worth the detour to Tbilisi for me.