Jilly's is a very nice place not far from Welsh-Ryan Arena, and although their Sunday brunch supposedly closes at 2 p.m., as d4v3 said, if you got a few others together, they might be persuaded to stay open. And it's small enough that it wouldn't take many to fill it.
Jilly's Cafe
2614 Green Bay Rd.
Evanston
If you can wait 'til 4:30, possibly the closest place to the arena is:
Trattoria Trullo
1700 Central St.
Evanston
Or, if you can wait 'til about 5, there's Chef's Station, a nice cross between elegant and funky, or Gio, for good Italian.
Chef's Station
915 Davis St., Evanston
Gio
1631 Chicago Ave.
Evanston
Or, at 5:30, you could get into The Stained Glass, although I imagine a new high school graduate might not be able to fully appreciate the wine flights.
The Stained Glass Wine Bar, Bistro & Cellar
1735 Benson Ave.
Evanston
Just a few random suggestions.