The only vegan meal option at the Oak Street Beach Cafe is a PB&J sandwich, which is somewhere in the $3-$4 range and comes from the fridge case (so the bread is usually slightly stale). The soft pretzels also aren't very exciting. They're pretty flavorless and tend to be dry. On the plus side, the Oak Street Beach Cafe is the only place in Midway Airport that doesn't have to custom make vegan options to order, so it's probably the best place to grab a meal if you're short on time.
In all honesty, I only eat here when I don't have enough time to eat at Harry Caray's. If at all possible, try to make your way over there instead.