I'm not quite as in tune with new Columbus restaurant discoveries, but I'll run down a couple of the exciting places that should be on visitors' radars.

Unfortunately, this place doesn't fit your bill because it's closed on Sunday evening, but the next time you're in Columbus, Harvest Pizza is a great joint in German Village. Nice little outdoor seating area, really high quality local ingredients, and perfect execution on the crust with a little char (typical pizza: fennel sausage, local gouda, smoked provolone, onion, fennel pollen). An ideal place for visitors (German Village is a charming place for a walk), the closest Chicago comparison would be Spacca Napoli with a little local flavor.

The most impressive thing I've eaten in Columbus recently was from a food truck, Ray Ray's. They've been operating and refining their product for a couple years now, and goodness is it refined. They have two trucks parked next to one another (one to handle overflow) in a parking lot just north of Ohio State's campus. There should be seating available in an outdoor patio at the bar the trucks are parked behind, but if you're looking for ambiance, this isn't the place. If you are looking for tender brisket whose flavor easily rivals Smoque (I can say this with some confidence), Ray Ray's is worth trying. As I recall, they have some very interesting beer tinged sauces as well, and Sunday they should be rocking the special grass-fed brisket, which is the can’t miss thing to order.

If you have specific things you're looking for in a Sunday dinner in Columbus (price range, cuisine, etc.), I might be able to provide more suggestions, because place closed on Sunday evening and a food truck may not be what you’re looking for. As far as a Monday breakfast is concerned, there are plenty of solid breakfast places in Columbus, but none that are can't miss. If you're looking for an offbeat but quintessential Columbus breakfast, you could seek out a Somali restaurant on Cleveland Avenue, such as the excellent Darbo, or one of the taco trucks on the west side, some of which will be open in the early morning. Columbus is one of the best food truck towns in the world, and not only do they have higher concept trucks hawking their food at a food truck warehouse called Dinin’ Hall, but the number of terrific Mexican food trucks on the outskirts of the city is staggering. Enough that there are a couple that serve breakfast as well—go to http://www.tacotruckscolumbus.com for a comprehensive guide to taco trucks in the city, but Otro Rollo and El Mananero are just a couple you could check out. If you're driving out of Columbus Monday, you might be best off stopping in small town Ohio for a slice of pie and bottomless cup of coffee for breakfast. Most every town in Ohio has one of these that you can sniff out (whether you follow the water tower, or ask directions for Main Street/downtown), and you’ll be in for an experience you can’t beat. See this thread on Balyeat’s in Van Wert for a great example of this: http://www.lthforum.com/bb/viewtopic.php?f=15&t=36812. Balyeat's is indeed a special place, but it seems like an Ohio diner as old as the town and steps from the county building pops up more often than not.
-TK

Harvest Pizza
495 S 4th St
(614) 824-1769

Ray Rays Hog Pit
2619 N. High St (behind Ace of Cups)
(614) 753-1191
Hours: Fri-Sun, 12-8

Dinin’ Hall
400 W Rich St
(614) 427-3560

Darbo (just one of many worthy Somali places to check out)
3764 Cleveland Ave
(614) 475-8004

Otro Rollo
3866 Sullivant Avenue
(614) 278-2339
Open 7 days a week. 7am-11pm

El Mananero
To the West of 3700 Sullivant Ave.
(614) 747-7051
Open 7 days a week 6 am to 6:30 pm