I don't live in the Valley now, but I did... and I've stayed in several areas since moving east, while vacationing.
The last 2 times we went to AZ, we stayed in Carefree/Cave Creek. There's little traffic, great riding, not tons of cars. Close to good climbing, too. And, close to north Scottsdale. Most places in the Valley (and I mean stretching 40 miles wide in every direction) are congested, suburban, strip mall sprawl. Maybe north Scottsdale, or out east of Mesa, but then you're surrounded by Leisure World people, no offense to anyone who lives there! I wouldn't stay anywhere in central Phx or downtown Tempe if the purpose of your visit is riding. While there are bike lanes and some paths, it's not cyclist friendly, at least compared to what I am used to. And remember, in April, it might be 90-100 during the day.