Great suggestions for Raleigh. But I think the ‘Canes home is a little ways west of the city, so I’m not sure if any of these places meet your criteria for being "near the arena," with the exception of Angus Barn.
Still, Murray’s should work for you and you owe it to yourself to check it out. It’s actually east of the city, but it’s just a short drive from an exit off the 440 beltway around the city. You can get right back on 440 and take it back to the arena area, avoiding the downtown traffic. Note, however, that Murray’s is only open Mon-Fri.