On my first trip to Japan as a grad student, we had a free day (mostly) to ourselves. A few of us wanted to ride the bullet train (Shinkansen).

We went to the station, went to the English-speaking window, and explained that "we didn't particularly care where we went, but that we wanted to go far enough for the train to get up to full speed" and get back in time for our evening obligations.

The ticket agents were very helpful, and ticketed us round trip from Nagoya to Toyohachi, also telling us she believed there was a local festival going on there. We went. We explored a bit. Had a great time. Easy to do.

You might have to venture a bit further out of Tokyo to really get up to speed. But, doable in one day.