Trip to Lomisi Monastery
Take a taxi or minibus (marshrutka) or hitchhike to the village of Kvemo-Mleta. The way up to the monastery starts near the church. It takes about 3 hours to hike up from the church down in the village. If you walk there the monks are happy if you bring up some food or something to drink. They are very kind and share their wisdom, tea and food with travelers.
For a detailed description of the trip visit https://snow.ge/de/events-activities/backcountry-in-georgia-guidebooks/backcountry-the-lomisi-monastery.html
Alternatively, Snowlab offers guided snowshoe hikes to Lomisi monastery, including avalanche beacon (pieps). It costs $30 and $50 if you would want to ride down afterwards. Snowshoe rentals cost an additional 30 GEL and 15 GEL for poles.
For more information see: http://snow-lab.com/en/lomisi
Trip to Stephantsminda (Kazbegi, 5047 m a.s.)
Stepahntsminda is just 30km away from Gudauri. You would just need to take the Georgian Military Road further towards Russia. On the way you will pass Jvari Pass (elevation 2379 m asl) which is definitely worth a stop.
To get to Stephantsminda, you can either take a taxi or minibus (Marschrutka) which costs around 5 GEL.
Once you get there you can hike to the Gergeti Trinity Church , which is definitely worth a visit and depending of the time of the year you could climb up Mount Kazbegito the Glacier. Mount Kazbegi is third highes mountain of Georgia, elevation 5047 m asl.
Day Trip in Gudauri
You can go on day trips within Gudauri, take up the lift and enjoy the view and visit some of the cafes and restaurants up there. Here is the description of one trip we went on:
We started our day trip from White Shino and went down to the Shino ropeway. From there we took the ropeway up the mountain and walked over to Khada Hut where you can, depending on the weather, sit outside and listen to Music and enjoy the sun or sit inside to warm up at the fire place and have a warm drink or dish.
Afterwards we took the Khudebi ropeway up to the top of Khudebi Mountain (3007 meters above sea level). There is another hut where you can either sit inside or outside on a terrace. Drinks and small dishes can be ordered. Up there you can watch the paragliders depart and walk over to the summit cross and enjoy the stunning scenery. After that we took the Khudebi ropeway and the following ropeway (ropeway 2) down and went to the restaurant Alubali, also known as the Drunk Cherry. It is right opposite of the ropeway station and they have all kinds of dishes, including a number of vegetarian and vegan options. After our visit at Alubali we took the lift up, walked over to the Shino ropeway which we took down. From there we walked back to White Shino Hostel.
The whole trip takes about 5-6 hours, depending on how long you are staying at those places. Pure walking and going with the ropeway takes about 2 1/2 hours.