Christmas Day, MSP
I don't know if they're doing it this year, but last year we were snowed in here and had a lovely 5-course meal at Cosmos. I had the traditional turkey with all the trimmings and I believe my husband had lamb chops. I'm not completely recalling his entree, but the whole experience was really lovely. I'd highly recommend it.
I have never been out to eat in the Twin Cities on Christmas, but here is a list from the Star Tribune of a number of places that are open. Also, searching for a reservation at the time you want on Open Table should give you a sense of what restaurants are open (although I might try a smaller party and then call if you have a bigger party as I have frequently found that the restaurants themselves are much better at figuring out if they can take a large group than the Open Table system is). Good luck and happy holidays!
I'm not sure which of these will be offering a nice, traditional meal--I'm sure that depends, in part, on what your traditions are (there are those for whom going out for Chinese food constitutes their Christmas Day tradition, for instance), but here's what's open per the Strib:
Manny's, Minneapolis, breakfast, lunch and dinner on both Christmas Eve and Christmas Day
Bank, Minneapolis breakfast, lunch and dinner on Christmas Eve and dinner Christmas Day
Chambers, Christmas Eve and Christmas Day (his writing is very confusing regarding what is available and when--I recommend just calling them if you're at all interested)
Cosmos, Minneapolis, four-course meal on Christmas Day
The St. Paul Grill, lunch and dinner on Christmas Eve and late morning to early evening on Christmas Day (it sounds like they are pretty well-booked, though)
Monte Carlo, Minneapolis, lunch and dinner both days
Market Bar-B-Que , Minneapolis & Wayzata, lunch and dinner both days
Shuang Cheng , Minneapolis/Dinkeytown lunch and dinner both days
The Lexington, St. Paul, lunch and dinner on Christmas Eve
Common Roots Cafe, Minneapolis, until 6 p.m. on Christmas Eve; open 9 a.m. to 4 p.m. Christmas Day
Rainbow Chinese, Minneapolis, open for Christmas Eve dinner
Bryant-Lake Bowl., Minneapolis, closed Christmas Eve, but open for dinner (starting at 5 p.m.) on Christmas Day.
Mickey's Diner, West 7th, St. Paul open 24 hours a day, 365 days a year
Flameburger, Little Canada, open 24 hours a day, 365 days a year
Additionally, according to the Pioneer Press, open on Christmas Day are
Champp's, W. Seventh St., St. Paul 4 p.m. to 2 a.m
Chez Colette (Hotel Sofitel), Bloomington; 10 a.m. to 3 p.m. and 5:30 to 10:30 p.m. Buffet
Hong Kong Noodles Restaurant, Minneapolis; 11 a.m. to midnight
Moscow on the Hill, St. Paul; 5 to 10 p.m.
Nicollet Island Inn, Minneapolis; 10 a.m. to 6:45 p.m., Limited dinner menu
Porter & Frye, (Hotel Ivy) Minneapolis; 6:30 a.m. to 10 p.m. Bar menu
Stockmen's Truck Stop, South St. Paul, Open 24 hours. Regular menu.
Tea House II, St. Paul; 3 to 10 p.m
W Hotel: Manny's, open 6:30 a.m. to 10 p.m; Living Room Lounge, open 11 a.m. to midnight; Prohibition Sky Bar, open 5 p.m. to midnight
Zahtar by Fhima, (Grand Hotel Minneapolis) Open 4 to 11 p.m. Regular menu and special prix-fixe family-style menu