Echo comment on Piestewa/Camelback's parking. Especially on Thanksgiving weekend, it will be very crowded. Most regular weekends getting a parking spot at either of these two peaks is a challenge. Despite that and the continuous humanity, these are pretty nice, energetic climbs, each with about 1,200 feet of gain. Piestewa has a better overall "trail" while Camelback has more low-end rock hopping and one section with handrails that sometimes scare off people although it's very safe.
The McDowell Mountains Preserve in Scottsdale/Fountain Hills are nice, probably won't be as crowded and not as far a drive out of town either. Also consider some of the peaks up in north Scottsdale/Cave Creek such as Pinnacle Peak, Black, Skull, etc. Many have SP pages. Much depends on your location; if you're in Phoenix proper or west in Glendale, consider the White Tank Mountains also. Most of the outlying peaks and ranges get moderate traffic. The urban peaks get a lot of traffic.