Wow - I would not choose either of those hotels (we were really unimpressed with the Westin Kyoto) but I guess you gotta use points when you can.
Freetokyoguides are awesome - took us all over town to see all the major sites. Also I would not rush to leave the Tokyo area, as a day trip to Kamikura was one of the highlights of our trip. Also since you are hikers you would probably enjoy the Hakone area which has some great hiking and views of Mt. Fuji.
For Kyoto I would highly recommend a paid guide - we loved Mayuri from
[email protected] The rate was quite reasonable and they will help you plan a customized itinerary. Ours included Arashiyama district including Tenryuji temple, Bamboo forest and Otagi Nenbutsu-ji and Nijo Castle. This worked well because some of these places would have been difficult to reach on public transit without a guide - and then you can easily find some of the more central places on your own. We also visited a sake brewery in a suburb just outside Kyoto - an enjoyable little excursion.
I would also recommend (as others) that you prebook your room for early am arrival instead of walking around in a daze. Maybe even an airport hotel so you can get off the plane and crash. Better to sleep in for a few hours, then head out in the afternoon and enjoy Tokyo at night.