I've been coming to Shaw Butte on and off for over 15 years. Never go to the parking lot off of Thunderbird. Best place that always has parking is the lot at the end of 7th Avenue, north of Peoria.
Do a lot of training for harder hiking & climbing and Shaw Butte is a great place to train. If you go up and down both sides of the mountain it's possible to put together a 5 mile hike with almost 2000 feet of elevation gain.
Have to thank the Phoenix Police Department, since they put in the sub-station in the neighborhood the park is a lot safer & cleaner. It was not unusual to see hookers and other assorted riff raff walking down Peoria early in the morning after a hard nights work. Have not seen any of this activity since the police moved into the neighborhood.