Walk on the Zuruldi massif

From Zugdidi to Mestia:
Marshrutkas to Mestia leave from Zugdidi train station every day. The first one departs around 6:30 a.m, after the arrival of the night train from Tbilisi, but there should be several others before noon. The last one usually departs at 14:30. The trip takes about 3-4 hours (1-hour break included) and the price is 20 GEL per person.

From Tbilisi to Mestia:
Few years ago, the best option used to be the overnight train to Zugdidi. However, it was cancelled in 2020 due to covid and there are no signs that it's going to be restored anytime soon. The only viable replacement is a long-distance night bus, which could also save you a lots of time, but won't be as comfortable as that cencelled sleeper train.
So you might have to stick to the day train. It departs from Tbilisi at 8:25 and makes it to Zugdidi at 14:10, just in time to catch some of the last marshrutkas to Svaneti. The price of the ride starts at 16 GEL, which is less than 5 EUR. Tickets can be bought in advance at matarebeli.ge website (the official web is railway.ge, but that never worked for me). Just one important thing - tickets are released for the online sale only some 15 days in advance. So don´t freak out if you can´t buy your ticket online because of the "no tickets available" error :)
If you want to save time, you could also consider a flight - there are 4 flights a week from Natakhtari airport near Tbilisi, operated by VanillaSky company . You would see Caucasus from a completely different perspective and for 90 GEL it´s quite a bargain. On the downside, they occassionally get canceled because of the weather and during the summer, you should book at least month in advance since they get booked up pretty fast. For more info, pls check this excellent post about the flight (covers also flight from Kutaisi).
The last option is the direct marshrutka - two minibuses depart at 7:00 from the area in front of Main Railway Station, come at least 30 minutes earlier to catch a spot. Another one departs at 8:00 from Samgori railway station. The price is 30 GEL, so it´s quite cheap, but I can´t recommend it since this uncomfortable journey takes grueling 9-10 hours - basically, it's just slower, marginally cheaper and less comfortable alternative for the day train.
So, if you prefer the bus, it's better to take comfortable long-distance buses operated by the Turkish company Metro bus. The downside is that they seem not to operate outside of the summer season and will get you only as far as to Zugdidi. There, you will have to switch to marshrutka to get to Mestia.

From Kutaisi to Mestia:
This depends on whether you want to get to Mestia from the city or from the Kutaisi airport.
In the first case, your best options is the direct minibus (the price is 25 GEL) departing from the station behind McDonalds. There is a fixed depoarture at 10:00 am but if you want to secure your spot, get there between 9:00 - 9:30 am. since it's quite popular among tourists. There may be also others during the day if there are enough tourists, but I wouldn´t rely on that. If you miss them and there is none other direct bus available, look for a marshrutka to Zugdidi (price 7 GEL) - it's the same way and you can find there transport to Mestia more easily (especially if you notify your driver in Kutaisi that you need to continue to Mestia).
If you are travelling directly from the airport, the most reliable way to get to Mestia used to be the Georgian bus (they have a stand at the airport) - the price was 40 GEL per person. But it got cancelled when covid hit and not yet reinstated. So you will have to ask taxi drivers loitering at the arrivals hall, they may be willing to give you even a better price.

From Batumi to Mestia:
Marshrutka is the only option, it departs from the main bus station. Since you will have switch the bus in Zugdidi (you may have to wait for several hours there), this ride takes a better part of the day. The first bus departs at 8:00 am, then there should be another one at 9:30 am.

The first marshrutkas to Zugdidi, Batumi and Tbilisi depart early in morning, around 7 am. every day in the morning at (these should be booked one day in advance). There are more during the day, depending on the demand. The last marshrutka to Zugdidi leaves around 19:00 and it´s ideal if you want to catch the night train to Tbilisi which departs at 22:15. However, since marshrutka schedules are not 100% fixed, better visit station in advance to confirm this and book tickets.
For exact timetables and booking of the tickets, visit the travel offices at the station. Just keep in mind that there are several offices and don't buy tickets too far in advance. We met tourists who entered the first office, bought there tickets for the next bus which departed in 2 hours and then had to wait even though there were several other marshrutkas (operated by another offices). If you can't find a suitable tickets and are not under a time pressure, I recommend just to grab a beer at the bar by the station, sit on the terrace and check the situation once in a while - sooner or later, some driver driver will show up.