I was hoping to take my bike on a (work) trip to South Bend, IN a few months ago. It would have been nice to have the bike to get around Chicago during an overnight stay between trains and then around South Bend.
Sadly, the South Shore Line - the commuter rail between Chicago and South Bend - did not allow bikes at the time.
It would be nice to have trains or even regional buses that go out and back in the same day. When I lived in Denver, I enjoyed riding out 30-40 miles and then catching a bus back home.