How to get to Kakheti from Tbilisi
You can get to Kakheti from Tbilisi by marshrutka, car or order a transfer.
The marshrutka will cost cheap. You can get from Tbilisi to Telavi for 7 GEL ($2.5), and from Tbilisi to Sighnaghi for 6 GEL ($2).
Shuttle service is a convenient, but less budget-friendly alternative, for traveling between regions. There is a convenient Gotrip service for this in Georgia. For example, a transfer from Tbilisi to Telavi costs about 40$.