Camping/fishing with family in ADK?

So with what I do for work I have very few extended weekend but July 4th I have a nice little 3 day weekend and I'm trying to find a place to take my better half and 4 year old daughter camping and fishing. I have tried to find a state run camp ground but due to the short notice there are next to none available. Does anyone have a primative camping spot they would recomend? Am I crazy for wanting to do this? lol I know of a handful of spots but I'm not sure they would enjoy them as much as I do. I did have a friend go to Moose River this past week but I'm told it can get crazy up there. If it was just me I would pack the truck and go but with the little one I dont dare do that lol