It should be noted that buying GPU's in Tbilisi is not a very cost-effective option, better use Amazon.com and service like usa2georgia.com to deliver your goodies to Georgia.
But if you are in rush, as I was today, and you are desperate to have a GPU right now, while in Tbilisi - there are several electronic stores I could recommend.
While I was still waiting for goodies from the US to be shipped to Georgia, I decided to buy an additional cheap GPU and put in on test at one of our spare office computers. Doing my due diligence I found Sapphire Pulse X560 4GB GDDR5 card at pshop.ge for GEL 499 (USD 187), unfortunately, I was not able to find this card on Amazon store, and I believe this card is sold in European and CIS markets.
Cat waiting for the first mining rig to be built
Another option was Asus ROG Strix GeForce GTX 1050 Ti OC Edition 4GB GDDR5 card sold at AltaOk store for GEL 779 (USD 292). This card though is sold on Amazon for just ~ $190. The savings are huge. I was able to track down this card at MetroMart store in Tbilisi for GEL 699 (USD 262)
See: Top 14 Best Selling GPU Cards 2018
As both cards promise a similar mining power (~11-14 MH/s), with GeForce version being a slightly better in most of the benchmarks, I still decided to stick with cheaper Sapphire Pulse X560 4GB GDDR5, probably by saving a $100 I made a fatal error, who knows. I'm planning to put this card to test soon and will share the results. Not sure yet, but planning to mine ethereum, zcash and monero, see: To Mine or Buy Ethereum/Zcash/Monero in 2018
There is a great comparison video on YouTube for both cards, see it here: Sapphire RX 560 Pulse OC 4GB Review vs. GTX 1050 & More
From my personal experience dealing with buying computers and computer parts, I would recommend following stores - AltaOk, MetroMart, PC shop.