Unfortunately, you are going to find little to no "real local personality" in Surprise. It is basically a good sized suburb that has sprung up in just the last few years. You'll find plenty of chain restaurants that you see all over the country.
However, if "your boys" are playing an away game and you have a free day from the park, I would suggest you get back on Grand Ave. and head northwest to Wickenburg. Plan on a full day here, it's worth it. This is a real old west town, and you will find a photo op around every corner in downtown. The houses, the stores, most of the government buildings are all the real deal. This is a great place to wear your jeans and boots. If you don't have them, there are a couple of good western stores right downtown to fit you with the entire gear.
You can ride horses at a dude ranch; visit the Vulture Gold mine which is really a small ghost town .
tripadvisor.com/Attraction_Review-g31405-d60…
Wander the streets for some grub and later some home made ice cream. There are several joints there with "real local personality." Everybody has their favorite. Here's a link for mine:
tripadvisor.com/Restaurant_Review-g31405-d51…
If that doesn't sound right for you, look here:
tripadvisor.com/Restaurants-g31405-Wickenbur…
Here are a bunch of other things to do in and around town:
tripadvisor.com/Attractions-g31405-Activitie…
Pay attention to the speed limit signs coming into town as they drop pretty fast and they mean it.
If you run out of things to do in town you can always hike along the beautiful Hassyampa river bed. Just don't drink the water or you will wind up like me. Would I lie to you?