suggestions for camping spots in Arizona White Mountains

Dan,
You can camp beyond the wilderness sign of either trail to Mt. Baldy (East Fork or West Fork), with easy access to the stream, and deer/elk wandering through the meadows. A day hike up Baldy, esp. from the East Baldy trail.

Dress warmly, it'll be freezing up there soon…

Can you drive up to those spots, or are they hike in?

The wilderness signs are usually about a half-mile from the trailhead, so the camping is walk-in, but very private, and only 0.5-1 mile before you find something you like… An alternative is that you can drive to one of the fishing lakes (check which ones have camping), but then you'll have to drive to any hiking.

hmmm that doesnt sound too bad. The reason I was thinking car camping was because I could still bring the luxuory items like an air matress and fresh tasty food. But 0.5-1 mile doesnt seem to bad….

Alpine area is nice, it has recovered well from fires. You can drive into Luna Lake, down Red Hill Road to the Blue River, camp there on the Blue River or drive to Hannigan's Meadow and camp there, established campground, and hike from there down into the Blue Primitive area, there is also Acre Lake which is right down the road 666 from Hannigan, all spots you can drive to and camp and hike. Stop by the Alpine Ranger station and get a map there and ask about these spots.
Any questions and y can PM me, I used to be a FS helitack employee out of Hannigan and Alpine.