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.
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.
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.