Definitely an experience
So temples, my favourite one is the Kiyomizu-dera which is in the hills overlooking the city. Golden temple is lovely but generally rammed with tourists. The streets down the hill from Kiyomizu-dera are fully of small pottery shops, some decent noodle places there too
Try this sake bar, i've not been but my parents went there last time they were there and raved about it:
http://openkyoto.com/postcards/kyoto-sake-bar-sake-cafe-hanna.html
The Nishiki market is worth a visit too.
Kyoto Sanga, the local football team, aren't very good, but the atmosphere was pretty good when I went.
Travel wise, make sure you get the Japan Rail Pass. It doesn't get you on the most current bullet trains but does get you on the Hikari I think, so you'll get to Kyoto from Tokyo in reasonable time.
In Osaka, make sure you try some of the Okonomiyaki. It originates from Osaka and was a street food.
Dotonbori is ace if the Hanshin Tigers (one of Osaka's baseball teams) wins, if they win the championship they jump in the river here. There's also a department store in Osaka which has a small ferris wheel in the front. It's a really strange store, used female underwear in a vending machine.