Guest House Borjomi Forest 

We booked a "Family room" for the 5 of us, and were happy to see there were two different rooms with a double bed in one of them and three single bed in the other. The rooms themselves were nice and bright, and we had a balcony with a great view of the city. The only downsides were that a couple of the beds were a bit short, and that the internet only worked halfway into the other room. Downstairs there's a kitchen where we cooked breakfast and dinner a few times, where they had everything we needed. The people working at the hostel were also generally friendly and helped us organise a trip to Vardzia. If you're planning on walking to and from the hostel, it takes maybe half an hour to get to the city centre, though we ended up taking a taxi most of the time, as it wasn't expensive (most taxi drivers don't know the Place though, so keep a map and the address at hand if possible!). When we were there, there were also some children that were being kind of loud outside in the late evening, but it didn't bother us too much.