Now to be able to travel to Georgia you do not need to present any PCR or antigen tests, nor proof of vaccination. This is the first country in the Caucasian region to remove all travel related restrictions.
All official information is published on the government website –https://www.geoconsul.gov.ge/HtmlPage/Html/View?id=2131&lang=Eng
To be fair to other countries, Armenia and Azerbaijan, their borders are also open, and any medical entry rules are not strict: either PCR test or a complete vaccination course. Read more details.
It is expected the land border with Azerbaijan will be open from 01 July 2022, currently you can enter Azerbaijan only by air.