Mark.
Unless you're trophy hunting, spend a full week in the Dallas/Fort Worth area. Play Jeff Brauer's TANGLE RIDGE, RIDGEVIEW RANCH, WHITESTONE, and SQUAW VALLEY-LAKES; John Colligan's SQUAW VALLEY-LINKS and HAWKS CREEK; and David Graham's and Gary Panks' (Gary Stephenson, primarily) TIERRA VERDE. If you want to play more than 18 per day, you can add SQUAW CREEK (Plummer), HARBOR LAKES (Phelps), MANSFIELD NATIONAL (Colligan), either of the TENISON PARK courses (Plummer, originally), CEDAR CREST (Tillie light, mostly Weibring), and a personal favorite, though a couple hours away, PINE DUNES (Morrish).
You can do all or most of this within your budget, including a rental car, gas, modest, but clean lodging, and good local food (and I know how much your son can eat). In terms of value (quality of the experience relative to cost), north Texas is hard to beat. You also will not feel more welcomed anywhere else.