Most touristy places (and non-touristy places, really) in Kyoto seem to close at 5PM or earlier, that's probably why there is a karaoke bar on almost every corner "downtown".
I'm not really sure what there is to *do* in Kyoto, I could never really figure that out myself, and have spent much time there. Always good to adventure I guess, it is so very unlike Tokyo, with very few of the "modern conveniences" that you may be used to if you spend a lot of time in Tokyo. If you have free time during the day, you should definitely explore the city... perhaps the most famous thing to see would be Kinkaku-ji (Golden Pavilion). There are dozens of historic sights in Kyoto that you could not possibly see all of in a week, let alone 1 day, but the Golden Pavilion is the most famous.
But seriously, almost everything closes ridiculously early in Kyoto, so start your day really early, too~ Pick up some Mochi (famous Kyoto "candy") inside Kyoto Tower (sold in a ton of different flavors), across from Kyoto Station (which in itself is an AMAZING piece of architecture, and the biggest train station in all of Japan). It is rather easily identifiable as the... well, the only almost modern kind of tall building in the entire city.
In Osaka, definitely check out Dotonbori, it is a bit "touristy" but it is also kind of the place to be at night. Maybe go for dinner at Kani Doraku, the best crab restaurant in Japan. Rather easily identifiable by a big moving crab on the exterior of the building.
Also make sure to try Takoyaki (fried Octopus balls), it will be hard to escape them in any form (even Takoyaki flavored soda...) while you are in Osaka. May as well give in to it.
And, you can observe the funny cultural differences between Tokyo and Osaka, which mix in Kyoto. Osaka and Tokyo are fierce rivals, and they seem to strive to do everything the opposite way of eachother. This includes standing on different sides of the escalator or moving sidewalk (yes, there are designated, unwritten rules for this!). It becomes mass pandemonium in Kyoto where people don't know where to stand because they mix and just stand everywhere...