I was in Georgia two years ago, and will be back next June as well (June 7-13 just in case).
First I should mention that Turkish Airlines also has some very cheap tickets to Tbilissi, less than 300 euros roundtrips (with possible stopover to tick Istambul WHS).
As for tips:
- renting a car is cheap, and driving around is not too difficult, close to southern Europe standard. It facilitates going around on a short time.
- 5 days is enough for Kutaisi, Gelati, Tbilissi, Mtskheta, with stop to Uplistikhe Cave Town (worth it) and Samtavisi Cathedral (500 meters from Kutaisi-Tbilissi highway; you have a quick glimpse to it from the highway).
- connections between Kutaisi and Tbilissi are easy, with numerous bus and marshrutka (collective taxis) or with own car.
- Gelati Monastery is about 8 km from Kutaisi town center, and very worth a visit (take a taxi). De-listed Bagrati is 1 km north of the main square (walk) but is very disappointing, having being restored beyong recognition.
- Davit Gareji Monastery is really worth a visit. It is easy to reach by car or with a travel agency. DO TAKE the road through Sagaredjo, and NOT through Roustavi. That last road appears on google maps, but is very very poor, and without any direction road signs. Once in Davit Gareji, do climb on top of the ridge and go to see monasteries in natural caves on the other side. Trails are easy to find. Cave monasteries are magnificiant. Technically, the other side of the ridge is in Azerbaidjan, but there is no control.
- In Tbilissi, the best areas to stay are around Liberty Square and Metekhi bridge. They are the touristic areas, lively, with shops, restaurant and cafes. I recommend Old Maidan Hotel, or Envoy Hostel.
- Mtskheta, try it on a Saturday, with cathedral full of weddings and baptisms.
- As for Upper Svaneti, it is more difficult to reach. Basically, one day to get to Mestia (5 hours drive), one full day with a guide to travel to the Upper Svaneti village of Chajashi, the only one included in the site (or with own car, but only with 4x4), and then one day to get back.
- To mention also: envoytours, in Tbilissi center, has well-organized day-tours to several destinations, including day-tour to Sanahin and Haghbat monasteries WHS in nearby Armenia.
- As for khachapuri, one is enough ! Do also try khinkali