Aside from the restaurants already listed, my guess is that anyplace in a hotel will be open. Some suggestions:
Augusta in the Westin Tabor Center. Haven't been there for many years, but it used to be excellent.
McCormick's in the Oxford. Part of the chain of upscale places, but consistently good.
Panzano in the Hotel Monaco. Like Megiac said, I'm not sure I'd be up for Italian.
OpenTable.com just sent out an E-notice of restaurants that are open that day. Here's the list:
Carmine's On Penn
Locanda Del Borgo
Maggiano's - Denver Pavilions
Miyama Japanese Steak House and Sushi Bar
Bent Fork Grill - Aurora
Maggiano's - Denver South
Jimmy's An American Restaurant & Bar
Marriott Vail - Ocotillo
Bent Fork Grill - Loveland