There are many campgrounds on Lake Pleasant - we stayed at Roadrunner which is near the Discovery Center.
We went there for an afternoon hike on the Roadrunner Trail and ended up going back the next day to stay a night during our RV Xmas trip. We lucked out and they had one site left. Then we REALLY lucked out because the site was water-facing and absolutely wonderful!
We tried to have a fire but a few minutes in the (very kind) ranger came by and said that we couldn't have a fire because it was a holiday. Odd. Apparently that is a land law and the state is trying to cut down on air pollution and it's a blanket rule of no fires on holidays. Again... odd.
But we still went on a great little walk and wandered around and found a hike across the road through the desert - just watch out for jumping chola!!!! We even saw a jackrabbit!
There's a dump station outside the campground area that is used by all the lake campgrounds, but there's two and it gets the job done.
You can also pay a small fee and just go there to hike or just go there to dump. The rangers are all super nice!