A helpful site you may to look at: Student Affairs | Housing & Residential Communities - Off-Campus Information
There, you can get tips on things you need to know about living off campus and can search for apartments that have gone through a vetting process with UA to ensure the apartments meet certain standards (Crimson Choice).
There are a number of off-campus complexes that cater to students who want to live off-campus but want the feel of being on-campus. I like to call them "condo colonies". Examples include the Retreat, the Reserve, the Woodlands, University Village.
Lots of people on here can also give you advice on specific complexes.