Upon my first time to the park, my nice wife bought myself & the family a birthday train ride. It was a nice overview of the park from the train. Good views of some eagle nests via trackside. It was also fun to see the railroad's shop from trackside. Ironically, the road parallels the track for quite a distance. Upon subsequent visits, we did explore the park via car that way. There is at least one waterfall that is not an easy walk from the tracks. One could always plan to stop at a visitor center or two via the train, but then one would have likely a bit of wait time for the return trip. It would take some planning.
I'm not sure I'd call a train ride a "must do". But I'm glad for having been introduced to the park that way.
If you will have a car handy, and you're in the mood for a National park experience, I'd suggest a drive to see president Garfield's residence on the northeastern side of town. Along the way, it's also a fun stop to see the house that they filmed "A Christmas Story" at. In the valley below the house, I think it's the Cuyahoga, is the rail museum & roundhouse where one of our Railwire members helps restore steam engines.
Just a few thoughts.