The hubby and I went here last weekend to see the Peanuts exhibit. He is a big Charles Schulz fan. I had pretty low expectations because 1. It's Mesa and 2. It's a kids museum. Not exactly how a dink wants to spend their weekend. But we actually really enjoyed the exhibit. There were a ton of kids there who seemed to have a lot of fun getting dressed up and playing with the props. The exhibit definitely had more to offer kids than adults. I would have enjoyed seeing more original drafts or signed pictures/copies. But the descriptions of character development and historical anecdotes of Schulz' life were really interesting.
Overall, it looked like this place doesn't have much to offer anyone over the age of five. But because of special exhibits like this one (the Jim Henson one Lisa N. mentioned sounds like it was cool, too), I may return in the future. Especially on a free admission day.