Fisch,
Enjoy Kyoto- it's beautiful. I recommend you visit Kiyomizu-dera if you've never been.
Digging for gold (aka old wheels and JDM grilles) takes a lot of time and without someone handy with Japanese and directions, might not be the best use of your time.
if you insist, try to locate a nearby Up Garage (2nd hand car parts seller) and they have a lot of used wheels, etc. Sometimes they have the good stuff like old SSR's.
If you to have spare time in Kyoto, I think a visit to the JDM master would be time well spent!
http://www.speedhunters.com/2013/08/the-house-of-style-tra-kyoto/
For what it's worth, I do bring wheels back as check-in luggage whenever I go to Japan, but 1) they are heavy! and 2) some airlines might charge extra depending on size/weight, so check before you go.
Good luck!