Yes there is a Sunni mosque in Tbilisi. It is located in vashlijvari No:29. If you take a bus number 14 from Baratashvilli it is fourth stop from Las Vegas bet (Peking avenue). read more
On the short walk up to the Botanical Gardens you pass the only mosque in Tbilisi that survived Lavrenty Beria’s purges of the 1930s. It's a red-brick building dating from 1895 and, unusually, Shia and Sunni Muslims pray together here. read more