Going to Athens end of October we have a full day before our cruise. Should we book a full or half day private tour and any suggestions on your company.
One full day to tour Athens is barely enough! Do the full day tour! You will want to return to see more of Athens.
Almost all the major tourist spots are located in the same area which is mostly pedestrian.
Don't take a Hop-on Hop-off, it's useless and you'll just go on the big (polluted) avenues
If you're looking for an organized tour, check out walking tours:
For example:
https://www.athenswalkingtours.gr/
https://www.alternativeathens.com/
RS also has an Athens City Walk audio tour in the "Listen" section: