My pleasure, Cubswin. A few more thoughts:

1. When are you going? That could affect some advice you could get here or elsewhere.
2. Also, what is your status at the hotels where you'll be staying? That could affect the advice you get re your hotels. You might want to include that in your FT ID information that goes with every post.
3. Now that you've nailed down the basic hotel/airline choices, you might pose specific questions in the Japan Forum here and at Tripadvisor.com's various Japan forums. (Just don't duplicate questions in this thread and that other forum, as that would violate FT rules.) As much as I value the FT community, sometimes I find the TA advice on specific destinations (as opposed to airlines and hotel chains) equally or more useful.
4. Not far from Kyoto, the old and somewhat less touristed historic Japanese city of Nara is well worth a visit. It's about an easy hour train ride away from Kyoto. We were fortunate enough to have an old friend show us around, but it seemed that finding your way on your own would be easy enough. Among the many highlights is an incredibly impressive, huge wooden temple and small deer that are so accustomed to people that they'll come pretty close without hesitation (though don't hold food near them or they'll reach for it!).
5. I would think that five nights each in Tokyo and Kyoto would be good. Assuming you are a Cubs fan and depending on when you are in Japan, you might want to look into attending a Japanese baseball game. It's supposed to be a real cultural experience. I'm sure the PH concierge can help if you can't arrange it on your own. I'd imagine the tickets might be expensive.
6. Actually, speaking of which, prepare for some sticker shock on many items in Japan. We found some excellent reasonably priced noodle shops that were great and some reasonably prices scarves and sweaters at little shops/stalls along the Philosopher's Path. But just accept that visiting this incredible country comes with a co$t. (If you have sufficient status at any of the hotel chains you'll be staying at, you'll save a lot via the complimentary breakfasts. If you can in fact get the Hyatt Diamond status I mentioned in a previous post, that entitles you to something like $75 per head (???) breakfast, for instance.)
7. Also be prepared that just about any hotel will be a letdown after the Park Hyatt. As I indicated, the Westin Kyoto is fine; but it's not nearly in the same league as the PH.
8. If you have Platinum status with Starwood, you'll get complimentary lounge breakfasts as well as late afternoon drinks and snacks at the Kyoto Westin. The main restaurant breakfast downstairs has a much larger spread, however.
9. The one bad piece of advice we got from the otherwise excellent concierge at the Park Hyatt was to say that just a very few days in Kyoto is sufficient. I'd say that your five nights there is a good plan, especially if you do a day trip or two.
10. I don't know enough about Osaka to know whether it's worth a night or two, as we did not make it there at all. If your flight out of there is late enough in the day and the advice you get elsewhere weighs against Osaka, you could even skip spending a night in the city entirely by simply seeing if taking a train from Kyoto and getting to the Osaka airport the same day is feasible.
11. Not sure where I'd recommend going instead if you do cut out Osaka. We spent three nights (IIRC) in Hiroshima and there is a decent and points-inexpensive Sheraton right near the train station. Visiting the city was pretty powerful, though for some reason I just was not that crazy about the museum. We also took a short trip on a (commuter-style) train and then a quick ferry from there a nearby island that I'm sorry I can't recall the name of.
12. In suggesting flying out of Osaka, I had in mind a non-stop flight from there to the USA. But your Osaka-Tokyo-LA itinerary sounds fine to me; it will save you the expense and most of the time and hassle that we had in taking the train from Kyoto to Tokyo and then on Narita.