Let me start by saying, I love Kennywood. It's the park I grew up with and the first place I rode a roller coaster. But that being said, if you can't ride many of the rides, there are only a couple of shows and they're not very good. There are a couple of arcades with average accessibility, some carnival-type games, and a tiny gift shop. The ambiance is good, though, if you like classic old-timey amusement parks. It's over 100 years old and listed on the National Register of Historic Places. The train ride features a number of pictures of Kennywood from days gone by (as well as some narration that I couldn't really make out). Kennywood is very conscious of its age, and celebrates it.
Maybe this reflects the limited number of amusement parks that I've gone to with my daughter, but I've never run across a process quite like Kennywood's. The first time a person with a disability visits the park and before they even buy a ticket, they have to answer a questionnaire (or have it answered for them) about their physical capabilities. A park employee will then fill out a sheet with what rides they are allowed to ride, which will have to be presented at every ride. On the up side, if the number of rides that are allowed is reduced, the admission fee is reduced accordingly. The admission fee for my daughter, who has severe disabilities, is $16. (Honestly, if I'd known this, we would have gone back to Kennywood sooner.) Once you've gone through this once, the park puts your information on file so you don't have to go through it every time. One notable ride that my daughter was able to do part of is Noah's Ark, a dark walk-through which is the only one of its kind left in the world. Also, the train has a car which can accommodate a wheelchair. One last accessibility issue of note is that the entrance ramp to the park is steep.