I live in Phoenix and if it was me thinking about the kind of excursion you are asking about I would rent a car, it may even be cheaper. Getting a cab at the Sky harbor will not be a problem. It is the getting one for the return to the airport that could be a problem. Public transportation is not one of our strengths. You could consider going over to Casino Arizona it is as close as any of the better malls and it would probably be easier to get a cab there, but you will need to call for a cab for the return to the airport. The malls and shopping on Scottsdale Road in Scottsdale would be were you would want to go. Google up Scottsdale and use the shopping feature it will give you all the information you will need.