I agree with hakata14, your plan is too much for a day in Kyoto. It will probably fill at least 2 days. Now the hard question is what to skip. And everyone will have a different advise on this.
Fushimi Inari then Kinkakuji then Arashiyama and Tenryuji maybe including the monkey park, ending in Kiyomizudera+Yasaka Pagoda+Maruyama Park.- think you can safely skip Kyomizudera as it is currently under renovation
Thus I would probably do:
- Ryoanji right in the early morning. It opens at 8 (or 8:30 depending on the month), be there right at the opening and head for the zen garden. It is best with little people around. It might be good to take a taxi from Kyoto station to Ryoanji, just because of your speedy travel style.
http://www.japan-guide.com/e/e3909.html- Kinkakuji: It is close by and you will be still quite early. There will already be crowds but Kinkakuji is wider and better to admire even with crowds
- Arashiyama (there is a small train line from the Kinkakuji area to Arashiyama, which in itself is a nice ride)
- If at the end of the day you see you are left with time, you can explore the sights close to Kyoto station. I would suggest Shoseien, a small garden.
If you want to get done as much as possible in the one day, taxi would be best, but you are 5... so you will need two taxis. At least I have never seen bigger taxis around.
You mention that you FLY to Tokyo. If you haven't booked yet the tickets, I would strongly suggest shinkansen instead. It will take less time overall. Maybe more expensive, depending if you got a discounted ticket, but the stations are centrally located, no check-in, no wait and if you miss the train you were aiming for you can take the next one. Just don't miss the last train, but that's after 21:00. So you have a full day in Kyoto and can even have dinner on the train (bento).
Enjoy your trip to Japan!