As other posters will tell you, there are lots of great places to live in the valley. Most cities have their good and bad parts. A realtor or long time resident can help you with that. The kidnappings and drug issues are isolated to certain parts of the valley and among certain "communities", it's nothing to be concerned about if you choose the right place to live.
Obviously your job location will somewhat dictate where you live, but if you're working in downtown Phoenix, Tempe or somewhere in the East Valley, my vote goes for Tempe as it's the most central you can get other than living in Phoenix. Tempe is home to ASU and there are plenty of houses for rent in Tempe. I haven't lived on the west side, but in the east valley, Tempe is as good as it gets. I worked in downtown Tempe for years and commuted by bike 6.7mi each way. I live a few hundred yards from the eastern border of Tempe in Mesa, another great city to live in, again if you pick the right places.
As far as riding opportunities, South Mountain (SoMo) is great and they have a monthly car free day (on sunday called Silent Sunday). I know many folks that ride to SoMo from Tempe, up, and back to Tempe.
Tempe is a Silver Level bicycle friendly community as designated by LAB (League of American Bicyclists). As I'm on the board with Tempe Bicycle Action Group (a local non profit in support of bicycling) we get to see the inner workings of Tempe govt in response to cycling and they definitely "get it". One of our board members attends the monthly multi-modal transportation committee meetings to give input and report on city initiatives.
Another thing to consider, if you want to make use of it, is the METRO light rail. You'll want to live in close proximity to the rail line for it to be "truly" useful.
http://www.raillife.com is a good resource for the light rail. Tempe has the added benefit of a pretty decent free local shuttle system consisting of 5 routes that cover most of Tempe (called the Orbit) and also light rail access points (
http://www.tempe.gov/tim/bus/pdfs/12.08OrbitWebMap.pdf)
I'd encourage you to to visit our website (link in my signature) as it's a good resource for bicycling all over the valley. Check our events & rides page for weekly recurring ride info, as well as routes, rides & racing for links to other cycling groups in the valley. If you have any specific questions feel free to post them, and if I can't answer I'll find someone who can.
Some good resources for public transit are
http://www.tempe.gov/tim and
http://www.valleymetro.org.
Best of luck!