This place is literally across the street from the Fox:
http://www.beststeakstl.com/It's a cafeteria style place, and it's definitely a dive, but the food is good. The clientele can be a bit "diverse" given the location (the Fox is right at the edge of the really shady part of town) but I've never heard of any issues there. I was a valet for a while a few years ago and often worked at Jazz at the Bistro which is a couple doors east of there. Dinner from the steak place was always the highlight of the night.
There's also Lucha (mexican) right next door. Although that place has been 3-4 restaurants in the last 10 years and the Best Steak House is still there...
Given that you'll be there for the Phantom, there will be lots of people about so I doubt you'll have any issues.