First of all, and this is standard advice in this forum, there is no need to change hotels between Kyoto and Osaka. They are less than an hour apart by train, and there are multiple routes.
Even if your flight to Okinawa leaves from Osaka (does that mean KIX or ITM?), you can easily make it there in time for your flight unless it leaves at 6:00AM or some other ungodly hour.
Since your interests are in history and Buddhism, spending more time in Kyoto than in Osaka makes sense. I think you'd appreciate a side trip to Nara, which was the capital in the eighth century and whose sights are conveniently located close together in a park-like setting.
Since you're making a one-way trip from Tokyo to the Kyoto-Osaka area and then flying to Okinawa, a JR Pass will not be cost effective.
Although Kyoto is more interesting for those who want to explore history and Buddhism, Tokyo is not without interest in this area. You might appreciate seeing a Kabuki play (you can buy tickets for individual acts, and there is English narration available via headphones) and visiting the Edo-Tokyo Museum and the National Museum in Ueno Park (drab and old fashioned, but full of things that would probably be interesting to you).
A daytrip to Kamakura, which was the shogun's capital in the early medieval period, would let you see the Great Buddha and more temples and historic sites. If you go on a weekend, you may be approached by a volunteer guide, a student of English who will show you around and will ask only that you pay for his/her admissions and lunch
There are entire guidebooks devoted to both Tokyo and Kyoto, including side trips, and you will have plenty of time to read them.
I've never been to Okinawa, so others can advise you on that.