For two weeks I would probably also recommend to focus on Kyoto and Tokyo and use these as bases to reach locations for day trips (such as Himeji, Nara, Nikko, Hikone, Kamakura). You can reach Osaka also easily and quickly from Kyoto to kake a day-trip.

The suggested Miyajima/Hiroshima might indeed be nice for a longer additional trip (i.e. staying overnight) My wife and I also had it on our agenda fro the trip we had planned for last spring (and then had to cancel).

If you you are fine with a somewhat longer trip to see a city that is quite different from Kyoto and Tokyo, I would also recommend Nagasaki - we have been there in 2003 and really liked it (the great weather and cherry blossom certainly helped)