Regis is a 10-minute drive from downtown Denver, which means that there are plenty of places to eat off campus. But if you don't want to make the drive, there are fast food places and sit-down restaurants unique to Denver right by Regis. Mead Street Station Grill and Bar has live music every night, good food, and is only a two-minute drive from the Regis campus. You can also look to the north, south, east, or west, and find some good Mexican food.
There is a wide selection of eateries around campus, but especially in downtown Denver. Around campus, you will see mostly Mexican eateries, but there are other types of restaurants, as well. Downtown Denver has whatever you could ask for in terms of restaurants. You will probably try many of these off-campus restaurants at some point, since cafeteria food gets old pretty quickly!