If you decide to extend your stay, another nice park in the same general area as Lost Dutchman is Usery Mountain Park. Its a Maricopa County park, but has a nice little campground with power and has some very nice desert hiking trails - they range from quite easy to medium hard.
http://www.maricopa.gov/parks/usery/
Another nice park between Phoenix and Tuscon which is good for anight or two is Picacho State Park. Again, some nice hiking trails and beautiful night skies.
http://www.pr.state.az.us/parkhtml/picacho.html
When your at Catalina State Park you might see some Roadrunners. While camping there once we saw around 30-40 at one time. They were hungary and appreciated the bits of cheese we gave them.