Re: Osaka & Kyoto recommendations
You should definitely not miss the opportunity to train with Okamoto-sensei - her classes are both fun and intense. Also, to me she seemed different from other Japanese instructors in Japan in some interesting ways, perhaps since she spent a long time training/teaching outside Japan (she founded Portland Aikikai).
Okamoto-sensei teaches at the historic budo center among other places - an interesting location to visit in itself. A number of other martial arts are practiced at the center and might be interesting to watch; I loitered in the vicinity of the kyudo range for a little while and was invited in by the sensei to sit down and observe part of the morning class. Fun if you haven't seen kyudo done formally before.
Also right outside the center, on the same street, is the Meirin sword store - excellent place to obtain iaitos/kenjutsu/kendo equipment. There are other gear stores just around the corner.
In Kyoto, I felt like I didn't even need to look for sightseeing locations; I'd just walk around and run into one after the other. . .