The most beautiful surrounding area of Tbilisi, to my mind, is Tbilisi National Park and Sabaduri forests from between Tianeti and Tskhvarichamia. You can enjoy deep beautiful forests on the road. In summer it is a nice place to escape summer heat, fry shashlik and rest. You can feel yourself in a fairy tale after a fresh snow, in autumn colors or in a mystic haze.
The area is less than 50km from Tbilisi, but to exit the city + the road even though its paved need in total 1 hour, After you start descending to Ghulelebi village you will find place of your taste. 41.922724, 44.926673 this coordinate few kilometers before and after you can search a place to stop and enjoy breathtaking nature.
If you are staying overnight in Kazbegi or Gudauri, from Sabaduri forests you can drive to Tianeti, then Zhinvali and continue day with exploring military road sights such as Ananuri, Gudauri etc.
In Ghulelebi village at the end of Sabaduri forests road you can enjoy local Khinkali and maybe drink couple shots of vodka to warm up in cold winter. Since the area became very popular recently. Saturday and Sunday mornings and holidays should be avoided not to get in traffic jam. You would not be surprised since the forests look so fairy tailish in winter.During October 15 +- one week it also looks perfect, even alley after Ghulelebi looks perfect in yellow colors.
From the magnificent forests of Sabadurebi you can also drive 30 minutes or take a bike trip to Sioni Lake and enjoy walking through the flower meadows in spring or bathing and relaxing on the lake shore. You can also try some bike routes outside the main road. One of the routes can be to Mamkoda Monastery which has some nice views and is closer to Tbilisi.
You will also find an unpaved road in the forest from lelubani village to Martkopi Ghvtaeba Monastery. One more option can be to camp in the yard of Bnela Sakdari church above Kevliani village which is a perfect camping place in Autumn.
You can stay in Sioni and enjoy your time there. It is popular area for picnic and swimming. Sadme cottages is the most recommended place to stay. Young lovely hosts who know how to party, like red wine and nice people.
You can also do a round trip and continue from Sioni lake to Kakheti side and return through Gombori highway. On the road you will find grand fortress of Bochorma. Bochorma fortress (X century) needs 30 minutes ascent till you come across great walls of the fortress. Inside there is a castle with has views to Iori gorge and st. George church. Inside church you will find traditional cradles which childless couples often leave there to ask st.George for help.
Hiking in Tianeti, Sabaduri Forest
As for Hiking in National Park – I did several hikes in Tbilisi National Park and will recommend it to my friends who are locals or stay here longer and want a weekend trip, especially during off season in winter or early spring, but those who travel from other country and have 1 week, I think they should not come here for trekking. Walking between Martkopi monastery and Lelubani lets say is nice but its not so special trip.
For the map and GPS of hikes in Tbilisi National Park please see (There is a road from Ghulelebi to Sioni reservoir I just wanted to show different roads):