Dixie Grill is a great breakfast for the no frills kind of mood. Andie, it's downtown on Market and is somewhat of a Wilmington institution, but with different owners through the years. Awhile back it was a breakfast spot AND a late night spot with a full bar, stage, and raucous punk bands at night. Now they have a breakfast menu (and lunch menu, too!) with the greasy spoon expectations and some more healthful additions. The atmosphere is authentic, a bar-and-stool set up runs the length of the place, the griddle is near the back but still behind the bar and visible. Tables and booths are also available. We've always experienced waits on Saturday mornings. It's not breakfast, but I really like their burger (nothing fancy, comes with skinny shoestrings). It's a healthy patty on a toasted bun, not greasy at all but not dry either. Just a good burger. I think it might be the best downtown can offer (apologies to Front Street Brewery).
We recently went to Chris's Cosmic Kitchen (Eastwood Rd) on a friend's breakfast recommendation (with chowhound support) and were impressed. The biscuits alone were worth it, and were obviously made fresh by someone who must have learned from grandma. They were the best I've had in awhile/ever?
For breakfast with a little more 'je ne sais quoi', we enjoy, and have nursed an unhealthy addiction to, Boca Bay's weekend brunch. It's extensive in selection and the quality is what you'd expect from the Circa/Brasserie/OC/Boca crew. It includes an accomodating omelet bar (split one, they're huge), a waffle station with bananas foster and grand marnier syrups, fresh fruit (the usual green & orange melon, strawberries, grapes), a stubstantial lox station, a decadent pastry table (if you like carrot cake save room, theirs is wonderful), and a hot covered station with the expected: bacon, sausage links, hashbrowns, eggs scrambled and florentined, and one more lunchtime-oriented dish that is usually a meat and pasta affair.
As breakfast prices go, Boca's is on the hefty side (I think around $12 a person, before drinks). And on holiday weekends that price doubles. Call ahead if you're going during the sunday post church rush to avoid waiting, though we've never had more than 15 minutes between us and breakfast heaven.
Go hungry. Go very hungry.
What about the place off College Road? I think It's just called College Road Deli. They serve authentic beef on weck that meets my picky new york italian eater's standards. I get the roast beef and horseradish there and it's very good.
Why go to Tayste and miss an opportunity to eat at Catch?
Bon Appetit serves dinner now (I think they've just changed their dinner hours to Wednesday through Saturday 4:30 - 9) and it is INCREDIBLE. They usually have cajun themed specials (~10$ a plate) on Saturday nights and dear god they are to die for. Their Po Boy is quite authentic and is very generous on the oysters for ten dollars... I had the catfish with veggies; it came with a dill cream sauce and the creole seasoning on the catfish was perfection. A couple of New Orleanian transplants were sitting near us and we couldn't help overhearing their praise (they had the catfish as well.) The complimentary bread is also baked fresh in house and is delicious... garlic knots, foccacia, and your standard italian comes out with pesto... I've heard the french dip sandwich is excellent from friends, as well as the Prociutto wrapped shrimp appetizer. I'd rank the calamari among the best in the city; very tender, served with marinara.
For everyone used to the bustle at breakfast, for dinner we go later (8ish) and it has been empty every time, which is wonderful for us but unbelievable since it is a top rate meal very reasonably priced. Service is notably better at night, and they've done a good job with getting a dinner ambiance. Go, but please don't tell your friends.