Downtown is very little, with only a bunch of tall buildings and not too many things to do.

There are some spots to see, such as the Arizona Science Center, where many interesting expositions take place (when I was there, there was one about James Bond's cars). Right next to the center, you can find a set with old houses representing Phoenix in the late 1800s.Near to the center is the America West Arena (home of the Phoenix Suns) and Ball Park One (home of the Arizona Diamondbacks). There are no shops at all (except for a gallery), but you can find several restaurants and cafés.

Bottom line: A couple of hours will be enough.