I stayed here for one night about a week ago. I'm a Marriott Platinum Elite, but come from the SPG side of the family so am not that experienced with Marriott properties - this was also my first stay at a Moxy.
Property is located in a new/purpose-built building on the east side of the river, but directly beside a bridge that walks you back over to the west side. The immediate neighbourhood is comfortable and not particularly noisy, although there's a small street that runs north of the hotel that's filled with cafes and restaurants.
The hotel itself was comfortable and had a nice feeling. The rooms were small, but the lobby was large with lots of different areas and a great vibe. Welcome drinks were offered on arrival. Bed was comfortable. There is very limited hanging space in the room, and I'd be careful about a long stay as there isn't too much storage. The hotel itself seems fully functional, although it looks like some additional retail or restaurants will open in the complex soon... the interiors remained under construction. The agent mentioned a gym being available at check-in, but I didn't check it out.
As a Platinum Elite, I was offered free breakfast. I'm not sure if that's only supposed to kick in once the programs merge in August, but worth mentioning. It was relatively simple, but a big big cut above the free breakfasts offered a some limited service properties in the States. Otherwise, the food choices are fairly limited. A bartender works in the afternoon/evening, so a full bar is available. I found drinks a bit expensive compared to a lot of other places in Tbilisi.
Overall, I felt it was very good value for the price paid (about USD70), and I would definitely return for a short stay.
Tbilisi is an outstanding place. I travel quite a lot, and would say it ranks among my favourite long weekends away, anywhere. I totally recommend it.