I'm afraid you might be SOL. We were in Anchorage this last Aug, and stayed at the Anchorage RV Park, which does you no good at all. We did drive around and look at all of the other RV parks in town, and they were not much. There is a public campground just north of town, clean, no hookups that we noticed, but it did have a dump station. For the life of me I can not remember its name, and I can't find our Milepost. As others said, you could boondock in one of a jillion parking lots in town. You could also go about 30 miles north to Wasilla, there are several full hookup parks there...
2002 Winnebago Adventurer 32V / 2004 Chevy Tracker