A municipal bus to the city leaves from the airport every 20-30 minutes 24 hours a day. It costs like a regular bus in Tbilisi. Then you will stop at any subway station. Go to Didube metro station, where the bus station of the same name is located. It offers cheap minibuses several times a day to the ski resorts of Gudauri, Kobe and Kazbegi. They do not have an exact departure time, the cost is about $3. The schedule is changing, so check the current one on the spot. Taxi to Tbilisi city center from the airport is about 30 lars/10 dollars. There is also an Aeroexpress train from the airport, which rarely runs in the morning and in the evening.
Transfer, taxi
If you take a taxi at the airport, it will be more expensive. If you take a taxi from the same Didube metro station or any other station, it will be much cheaper. The inscriptions on minibuses are only in Georgian, you can ask someone to give you a hint. However, taxis in Georgia are much cheaper than in the whole world. When ordering a taxi through an aggregator, applications like Yandex/Maxim, you can get to the hotel itself comfortably and relatively cheaply. Public transport may be specific to Georgia, and most likely you are not ready for this. If you are traveling with luggage, ski/snowboarding, and plan to travel safely and comfortably, please book a transfer.
On your own
On the Tbilisi-Gudauri route, the distance by car is 135 kilometers, and the city is connected by the Georgian Military Road.
From Tbilisi
Local buses run from the airport 24 hours a day, there is no fixed schedule, but it will be easy to leave. You can also book a transfer from Tbilisi to Gudauri at your hotel, almost everyone at the resort offers this service. Or take a taxi upon arrival at Tbilisi Airport. A private transfer from Tbilisi Airport to Gudauri will cost from $40 per car. Many local companies offer car rentals for tourists. It is better to specify the conditions in advance so as not to be left without transport. There are rental offices in Tbilisi and Kutaisi.
From Batumi
You will need to get to Tbilisi first. This can be done by bus, train, minibus, and sometimes on a small local plane. The train is fast, but it rarely runs, literally in the morning and in the evening, the journey takes about 5 hours. The bus station is located on the other side of Batumi. The train station is even further away, and it will be easier to get from the airport by taxi. There are private buses like 'Metro' that leave oddly enough from the train station. Minibuses depart from the old bus station. It is difficult to say what the flight schedule depends on, and it may simply not exist. You should not count too much on the plane.
From Kutaisi
The 225 km journey from Kutaisi to Tbilisi will take about 4-5 hours. The train is extremely rare. Please check the departure time in advance. The easiest way to leave is by bus, they adapt to the flight schedule. The minibus to Tbilisi leaves approximately every hour. You can also book a transfer from Kutaisi-Tbilisi Airport for approximately $15. If you are very lucky, it will be possible to fly from Kutaisi by private jet, as there may be no schedule or regular flights
From Vladikavkaz
There is one road from Vladikavkaz to Georgia, which turns into the Georgian Military Road at the Upper Lars border crossing. It is forbidden to cross the border on foot, only by car or, for example, by bicycle. You will need a driver's license and a car certificate to get from Moscow to Gudauri. The risk is that the only checkpoint on the Russian-Georgian border may be closed due to an avalanche or threat of an avalanche. In winter, this happens all the time, but if you want to get to Gudauri on a budget, you will have to take risks. Georgia has few gas stations and no winter diesel engine. Check the condition of the Georgian Military Highway in advance so that it is not closed at the most inopportune moment. Cars registered in Crimea are not allowed to enter Georgia.