People usually visit Nara, Kyoto and Osaka together because they are right next to each other. You can explore them within two days conveniently using the JR rail as the main form of transport. There are tons of temples and traditional Japanese cultural sites in these three places, including the Genjimonogatari museum. And in Nara, (mainly stupid) deers too who eat everything. And you have a really nice Osaka Castle too!
Here are some pictures:
And last but not least…an Osaka castle in its monochrome splendor.