When you first move to Tbilisi you will spend a lot of time figuring out where to buy those elusive things (food and home) that you long for. While not everything is available here, most of it is hidden is different markets and stores around the city.
There are two main “western” supermarket chains: Carrepour and Goodwill. The Carrepour at the Tbilisi Mall is the largest of them all and is your best bet for finding uncommon things. The meat and fish market there is also very high quality. The Goodwill store in Saburtalo also has a good selection of things and it is more centrally located than the Tbilisi Mall, which is quite far north of the main town.
Some things you will NOT find: molasses, brown sugar, most tropical fruit (passionfruit, papayas, starfruit, etc.). Some things will be difficult to find: maple syrup, quinoa, duck, pine nuts. The things that are difficult to find (read “uncommon here”) will be relatively expensive; often, ridiculously expensive:
Some things you will see and may not recognize at all, but you will learn to love them: sea buckthorn (კაცვი), cornelian cherries, various forest mushrooms (always wild), marigold flowers, blue fenugreek and Svaneti salt. Some things you will gawk at but probably not buy: whole pig’s heads, chicken with the head and feet attached, and internal goodies from that cow/pig/lamb that you will never see for sale in the sanitized US markets.
I finally worked my courage up to buy meat at the market after several trips. There are entire carcasses lined up for “show” and you must generally speak enough Georgian or Russian to convey which of the bits you’d like to buy. But by American standards, it is quite inexpensive and to my eyes appears to be very good quality. Beef, pork, lamb and chicken are readily available. Small Cornish game hens and quail are also available occasionally. An entire beef tenderloin which would set me back $100 at Costco in the US costs $10-15 per kilo, a fraction of the price.
Fresh herbs are interesting here. You can buy most of the ones you are familiar with (seasonally), but tarragon is king. It is used here more than any other herb and you will always find it in the market, neatly bundled between two sticks and always of very high quality. Only purple basil is available; it appears that the sweet green basil we are used to is unknown here. Thyme is… a problem. You buy thyme (კონდარი), but it will always be dried, on long stalks and poor quality. Mint and basil and many other herbs are usually only available seasonally, so you might not find them in the winter. Available year-round are cilantro (the other Georgian staple), flat-leaf parsley, dill, and the ubiquitous tarragon.
For root vegetables, other than potatoes, you will generally have one variety to choose from. Only red beets, for example, seem to be available here, and you will rarely see the greens still attached. Potatoes come in different sizes and colors with some variety. Onions as well come in several different colors and sizes, and pearl onions are easily found.
Celery is hit and miss here. I have only found it at the Goodwills in Vake and Saburtalo, and sometimes they have it and sometimes not. I have to keep my eye out, because the biggest deficit in “cooking supplies” here is stock. You will not find chicken, beef, vegetable or any other stock in the grocery aisles, in cans or boxes, though you can buy the dreadful Magi cubes. You must make your own, which is, of course, the best anyway. But it is something that needs celery!
If you want golden or candy cane beets, sweet corn, thyme or any number of other “rareties” here, you will have to set up a little garden. I am fortunate to have a 25 square foot terrace where I shall plant many seeds this spring!