Maybe too late for this, but Oasis is one of my favorites. Very new-age type of place, but also very hipster. They have a bookstore attached to it too (Golden Braid bookstore) if you are waiting for a table, and during the warmer seasons, they also have courtyard outdoor seating.
151 South 500 East
oops.... Oasis is not a chicken type of place
. Ruth's diner up Emmigration canyon is nice, and a cash-only place that closes at 2PM on 3300 S / 2300 E called Over the Counter is pretty good too.