Citizens of more than 100 countries do not need Georgian visas, including the US, EU and almost all European countries, formed SU countries, Israel, Turkey and many others. 

Covid Entry rules for foreign citizens travelling to Georgia are quite simple:

There are 5 interantional airports in/near Georgia : Batumi, Kutaisi, Tbilsi, Rize/Artvin (Turkey) and Trabzon (Turkey). 

Distances to Batumi: 

Kutaisi - Batumi 120 km, Tbilisi - Batumi 360 km, Rize - Batumi 80 km, Trabzon - Batumi 150 km. 

There are daily  flights from and to Batumi airport - Istanbul, Minsk. Tel Aviv, Baku and many others will be added by the 1 April, 2023. 

There are many daily cheap flights (including Wizz Air) from and to Kutaisi airport - Milan, Paris, Krakov, Vienna, Barcelona, Rome, Abu Dhabi, Minsk, Berlin, Vilnius, Athens and many others. Some will be added by the May, 2023. 

Tbilisi is a capital of Georgia.

There are many daily cheap flights from and to Trabzon airport, mostly Turkish cities - Istanbul, Ankara, Ismir and many others. There are 2 flights from Germany - Stuttgart and Dusseldorf. 

There are many daily cheap flights are from Isanbul, Ankara and Tashkent.