Mama Terra caters to a small, niche audience, but offers food that even a carnivore could love. 

Their juices and smoothies are particularly good (and very healthy!). 

Located in the Sololaki-Mtatsminda neighborhood, the prices are on the higher end but as to be expected for central Tbilisi, and, as they say:

"Our mission is to have an alternative brand to which healthy conscious people can identify without compromising flavor in a relaxing atmosphere with a varied selection of healthy, vibrant, colorful, affordable and delicious vegetarian, vegan and raw food."