The better the area, the higher the price. I'm finding it difficult to believe that there is "no crime" in Arizona.
Best bet for crime inquiry: http://www.crimemapping.com Just type in the address and it will show you reported crime - you can change the date range also.
EVERY city has crime, which is why every city has a law enforcement agency.
Crime can vary from violent to non violent, but crime exist everywhere on some level.
If you want crime stats for Lancaster Ca contact the LA County Sheriff's Department. They police Lancaster. They are the BEST source for crime stats.
Best of luck to you on your move!
Kawain Payne, Realtor
Berkshire Hathaway Home Services
Also check this link for Quartz Hill:
I will be more than happy to help you find any additional information.