The Children's Museum of Phoenix is a little young for a 9yo, but sometimes my 9yo likes it. The science museum is across the street from it, near the ballpark.
Smeeks is an awesome local candy store at 1st Ave. and Camelback. Good place to stock up on chewy candy for the plane ride or have a really good time spending a couple dollars of allowance. My 9yo is a fan, and likes to claim that visits help build her arithmetic skills.
Smeeks is near Pane Bianco, which is the takeout-only lunch and dinner place just south of Camelback on Central Ave operated by the owner of Pizzeria Bianco, which supposedly has the best pizza in the US but has a line too long to be stood in with little people. 11-8 T-Sat. The sandwiches are awesome. I didn't actually know they had a dinner menu until just now when I looked up their address, but apparently they do. They do not have tables.
Sonic Drive-ins are all over Phoenix. They (sometimes) have the funnest happy meal toys ever, a massive selection of soft drinks, and the servers roller skate to your car. A good place for cherry limeade and soft-serve ice cream. The tater tots are scrumptious, and again, my 9yo is a fan, especially on long drives.
The Phoenix Art Museum recently underwent some renovations and is friendly to 9yos if the 9yo in question likes art. At the moment, there is a huge red plastic dinosaur on display on the front lawn.
There are a lot of parks in Phoenix. My favorite is Dreamy Draw, on Northern just off rt. 51 (take the Northern exit and then turn east - the road dead ends at the parking lot/trail head). Nice hiking. Restrooms, but no concessions - bring water.
The zoo has teenage zebras, and you can feed the giraffes and pet the stingrays.