The Cleveland History Center is definitely not quite as popular as the other museums in the area, which is also probably why I never went until my final year at Case. What finally attracted me was passing by the carousel so many times and hearing that you could ride it for free (included in your $9 admission).
Now the museum is quite large and is made up of several different parts. Honestly some of the exhibits were not really interesting to me. However I would say the large collection of cars is a must see (although if you're not that into cars avoid going with someone who really likes them because you might never leave), and the children's exhibit area is actually kind of fun and interactive for a short time. Additionally, we bumped into one of the staff workers as we were walking through the Hay-McKinney Mansion, who ended up explaining lots of interesting things about the history of the place. Make sure you walk out to the garden(?) area, which allows you to see how big the buildings actually are because it is hidden from outside the museum. And of course, the carousel is always fun (but I've always loved carousels anyways).
I can definitely see why the museum is not as popular for the general public, but I would say it is worth checking out at least once (especially if you are a Case student and have free admission). It's not a place I'd go for a second time, but I enjoyed myself more than I thought I would the first time!