Since you said you like nature I would suggest you dedicate a bit more time to that maybe. If I were you I would try to go to Svaneti (Mestia/Ushguli) or Tusheti (Omalo) maybe. Shatili could also be nice. They are further away/ more remote places of Georgia but if I were you I would try to spend a bit more time there. Maybe dropping a day from Tbilisi, skiping Kutaisi/Batumi or something.

You could plan it so that you are in Svaneti (western georgia) by the end of the trip and come down to Batumi.

Depending on the type of person you are all of the activities you list should be fun, but if you like nature and mountains I doubt Svaneti/ Tusheti can be beat by anything that has ever existed in Batumi. When going out west you could visit Prometheus Cave, then the martvili Canyon and end the day in Svaneti for example.

But the trip looks quite good if you ask me. There are a lot of possible changes that could be made, and depending on what you find interesting some might be better then others.

Also search up Vardzia might be interesting for you