Week 2 east Georgia
Train to Kobuleti, book one of the nicer but still cheap hotels like Aquamarinn at the shore line. Get used to the place and you can have a swim that day.
Drive to Batumi botanical garden, it's a big one and will take up to 3 hours to explore, then drive to Batumi, you can eat at generic spots like Grill town. I suggest just exploring Batumi as a city and not swimming there, all other mentioned places are superior for swimming. Taste Adjarian Khachaluri at Retro. In the evening on the way back you can eat some fish at Fishlandia.
Drive to Dendrological park, on the way there pack food for the day from Kobuleti not that many good stuff up there. After Dendrological park to to a beach in Guria like Chakvi right there and relax for most of the day, beaches there are clean and water is very nice and warm usually with small pleasant weaves. It is also magnetic sand beaches so allegedly it has some health benefits. Drive back to Kobuleti, usually if you become friends with locals at the inn they will make every evening fun for you.
Get a tour to drive you around historical places in Adjara, various caves, Gonio fortress, Dandalo bridge, high mountain villages, waterfalls etc. Every evening and morning can be supplemented with just chilling at the beach.
Drive to Guria again but this time go hiking to Gomis mta and it's surroundings for the whole day, it will be a great trip.
Go to Batumi again, book Dolphinarium visit and you can try out one of the more fancier restaurants like wine restaurant marani.
Train back to Tbilisi and fly back.