If you want to walk, a lot of the places being recommended are a several block hike. Not too bad, but it depends on your party.
A place I haven't seen mentioned is Sons of Liberty. It's more coffee shop than restaurant, but quite a bit cheaper than the other options listed. Although, if you're staying at the Omni, I'm guessing price is no issue.
Their coffee and pastries are magnificent.
EDIT: If you're going to drive, consider going to the near southside and try Hot Box Biscuit Club.