Kyoto would be great. Another suggestion, if you are interested in just having a look around a slightly smaller city rather than going to specific tourist spots, Kobe is a nice place to just take in the urban landscape. Dead easy no brainer to get to/from Kansai via limousine bus straight to Sannomiya. Some pretty good shopping, pleasant walks to the waterfront etc. Low key, but it my fit the bill depending on your interests.

Have a great trip.