Hiroshima might be a good place if you are into Historical sightseeing. There is a world famous "the Atomic Bomb Dome" , its also called Hiroshima Peace Memorial.
and Itsukushima Shrine is also a must-see place!! This place is famous for a giant floating red gate in the sea.
If you are interested in Onsen, Hakone is pretty easy to reach from Tokyo with about an hour by Romance Car Express Train. Some more interesting places that is reachable from Tokyo would be Kawagoe in Saitama prefecture. Kawagoe is also called Ko-Edo meaning small Edo, where lots of old buildings left.
I recommend to visit Kanazawa and Nagano by taking a new shinkansen (fast bullet train). In Kanazawa, you can enjoy seafood, beautiful traditional park called Kenrokuen. Also, in Nagano, you can enjoy soba and histrorical huge temple called Zenkoji.