If you're a museum buff, just plan on spending the whole day here. I came on a Saturday and was here literally from open to close. There's SOOOO much to see!! Dinosaurs (I want to say the tour guide said this museum had the most dinosaur bones out of the whole US?), gems, mummies, statues, paintings. This place seriously has a little bit of everything. It was kind of overwhelming.
Parking is a flat rate on Saturdays in the museum parking lot ($6, I believe). Other days, it's hourly.