Keep in mind that the weather might be changing very quickly and especially in the mountains. If it's warm in Tbilisi/Kutaisi it won`t necessarily mean that it will be the same weather all over the country. Some areas of Georgia might be windy. Hiking waterproof shoes is a must for some regions and some abandoned locations.
October in Caucasus is usually pretty refreshing, but could be also tricky; be prepared for the range of +17
°C during the day if sunny to 0
°C (at night, or on a higher altitude).
Your phone, camera, tripod (not mandatory, but really useful, specially inside abandoned buildings and dark spaces).