I love to park on Superior and take people to the Arcade and the libraries (and seasonally the Eastman Reading Garden). You could add the Federal Reserve Money Museum at the same time, as it's right there.
I always take visitors to the Museum of Art, a great way to see something fabulous for free.
I also second the notion of Li Wah for dim sum. Incredible to say the least! Another foodie location that I just love is Lilly Chocolates in Tremont. Plus, they can see St. Theodosious at the same time.
And, I always like to take a walk on the east bank of the Flats. You can park under the bridge near the RTA station for like $2.50, though I don't think they patrol the lots at all on weekends unless there is an event going on. It's very quiet in the morning there, just some people walking dogs. There's usually one or two people sleeping there, but I've never been bothered by anyone, even when I go alone.