Kyoto's structures definitely have an older feel to them, while the architecture in Tokyo and Osaka is newer. Kyoto was built on a grid pattern, and the city still retains that structure. While Kyoto does have a lot of shrines and temples (and is a popular destination for the tourists who want to experience traditional Japanese culture), the city is still very modern, and there are lots of shopping districts. It all makes for a very interesting fusion, because as AKyber said, Kyoto didn't incur much damage in the war.
Tokyo is where I lived when I was over there. It's pretty packed: space is at a premium, so an average income family will probably own an apartment, not a house. Most people use public transportation, even if they own a car, or they commute by bike. There are parts of Tokyo that are pretty much always crowded - Shinjuku, Harajuku, Shibuya, and Akihabara, to name a few - but there are quieter parts of the city, too. Hikarigaoka, where I lived, is almost suburban, and it has a gorgeous park.
I've only been to Osaka twice, sadly, and never for a full day. They do speak Kansai-ben, which is extremely distinctive, and Osaka has a very strong food culture. Okonomiyaki is probably one of their best-known dishes. (Because it's AMAZING.)
Best of luck! Feel free to PM me if you have any specific questions, especially about Tokyo - I'll do my best to answer them!