A few of the communities have golf cart paths that you can take to the corner grocery and drug store ("Power Center" in builder talk). City Bus Service is rare so you may have to use taxis. Some of the adult communities have their own private small bus service that makes scheduled runs to shopping centers. Some communities allow golf carts which are street licensed, but you have to have an AZ driver’s license to use them on the streets.
check out the Valley’s Public Transportation website