Definitely visit the Sonoran Desert Museum.
http://www.desertmuseum.org/ It is quite a drive from Catalina State Park, but well worth an afternoon or morning.
Another interesting place is the Pima Air and Space Museum. While there I took a tour of the "boneyard" which is where the military stores old planes and breaks them up for parts and scrap.
http://www.pimaair.org/There is lots of large vehicle parking at both places, but I do recommend that you do not let your GPS take you to the Desert Museum through the Tucson Mountain park on West McCain Loop Road. You are better off going the slightly longer way. I think it was Via West Mile Wide Road and S. sandario Road. Ask around. I have a 32' Class C and did not like the tight turns. If yours is smaller, though, it might be fine.