We visited Hakone/Lake Ashi for a couple of days when we went there. A nice area if you want to see Mt Fuji (from afar).

Kyoto is beautiful as well (streets are organised like Melbourne CBD). If you do visit Kyoto, stop by the Arashiyama area.

In terms of old castle, I think Nijo Castle in Kyoto retains a far bit (ie. not allow to use flash photography)