Tempe Diablo Stadium, while having a good deal to recommend it for viewing the actual games, has very little to recommend it for anything else. For one thing, its location does not lend itself to those wishing to save a few dollars and food and beverage before going in the gate. Let's face it, short of Top of the Rock (an upscale, expensive fine-dining establishment), located in the Marriott Buttes Resort, there isn't much at all in the immediate area in terms of food and drink options other than standard fast food fare. If one is looking for something in walking distance, even Top of the Rock, which overlooks the ballpark, is not really an option, as one has to walk all the way out and around the resort to get back to the ballpark.
However, the beer and food pavilion inside the park out on the left field concourse is actually not at all bad, and at least as of last year, was reasonably priced b ballpark standards. For those looking for dining in the vicinity of Tempe Diablo, the best options are post-game options. One of the best and most popular post-game destinations is Claim Jumper in the south parking lot of Arizona Mills Mall on Baseline, just east of the I-10. Here, the house brews are both tasty and cheap, and the food is a slight cut above the others in the area. For those not into house brews (they have four on tap) there are about 12 other beers on tap and a very large bar and lounge with a full offering of adult beverages. Though I have asked, it seems that nothing definitive for this year has been decided yet, but in past years, game tickets brought discounts as well.
Inside Arizona Mills is Rainforest Café (also owned by Landry's, the owners of Claim Jumper for all you Landry's card holders). The bar here is less attractive, and the food is much more expensive. It does however provide a great deal of entertainment for kids that the other places may not, save one, which is...
Game Works, located in Arizona Mills right next to the Harkins IMAX. The bar here is small(ish), but the selection of beers is acceptable and the price is not half bad. The food is pretty average, but let's face it, pizza is very much a personal thing, so maybe others will love it. Of course, the real draw for Game Works is the video game arcade, which has all sorts of offerings for all ages.
Going the other direction from Tempe Diablo, one can find Philly's Sports Grill on Priest, just north of Broadway. Those that have frequented the area in the past ay remember the place as, Hail Mary's on Priest. Here, the food is hit-and-miss, ranging between "passable for bar food" and "damn tasty". There are televisions for sports everywhere, including small monitors for each table. The beer selection, while by no means anything special, is very adequate, and the pricing is pretty fair all around.
Of course, none of these places are strictly post-game hangouts. One could just as easily go before a game as well, though none of them specialize in getting people in and out quickly, so going before a game needs to be well planned.