I don't think there's much around Suzuka, really, but going just a bit farther north to Nagoya will put you on the Shinkansen route, and then you can take yourself to Tokyo in 90 minutes or to Kyoto in less than an hour.

If you're into Japanese history and culture, you could travel south from Suzuka and visit the Great Shrine of Ise, one of the imperial shrines, but if you're not, you may be unimpressed.

Near Ise is Toba, home of the Mikimoto Pearl Company, which has an industrial tour and at least used to have an exhibition of traditional pearl diving.

Traveling west of Nagoya on a local train will bring you to Hikone (not Hakone, Hikone) on Lake Biwa, which has an well-preserved original castle.