First off, I am a regular at Prairie Joe's who was formerly a regular at Kims' and prior to that a regular at Lucky Platter. Basically, my choice of breakfast spots has to do with proximity to my home. All in all, I'd say that Prairie Joe's is the best choice of the three you mentioned, though there may be better choices, depending on what you want. I enjoy Prairie Joe's Mexican- style breakfast offerings. I say Mexican-style because I cannot say how authentic they are, but I like the breakfast chorizo, egg, and cheese burrito and the huevos rancheros. The parking is quite difficult, and the coffee is weak, but the art and funk factor are superb, and I like the owners. I wish they had Kim's muffins or some other homemade pastries. The Southern Breakfast with ham, eggs and grits is good, but I can't say much for the biscuits and gravy. (I guess they need a baker). Although I eat breakfast there pretty often, IMHO, their lunches (with many daily specials) are where they shine, but that's another thread.
I'm sad to say it, but Lucky Platter, for me, has lost some of its earlier (much earlier) luster and I am not sure why. Maybe it's just that my daughter is grown up and I miss the vision of her in four-year-old finery twirling in between the booths. Even so, their classics seem a bit tired to me. Their menu, which seemed hip and rustic 13 years ago, (like the sweet potato fries, the sandwiches, and the veggie hash) now seems heavy and in need of a good overhaul. At breakfast, they have granola and a pretty wide choice of fillings for the omelettes, but I've found the coffee often burned and the pastries not as good as they once were.
Kim's has the best muffins and scones in town, and tends to be very calm and a good place to read the paper, but it's really more of a bakeshop than a restaurant. Kim's doesn't offer eggs and sides and a bottomless cup of coffee. The protein and caffeine are important for me if I want to call breakfast a meal.
Another choice for you could be Blind Faith. Here is a spot that, in spite of its admittedly retro elements, seems to be quite well-managed and
continues to update its menu, while retaining old favorites. To my mind, the best breakfast in Evanston is the Mexican Breakfast with
Scrambled Tofu and Cheese, Rice, Beans, Salsa and Tortillas. It's expensive, but will easily satisfy two people. They also have excellent fresh juices and blueberry muffins. Best of all, it's not too crowded on a weekday morning--but check for their hours, as I recall being disappointed once when they were closed. BTW Coffee is decent, but the kukicha tea is better. Two coffee houses, Starbucks and a local purveyor are within a block. Street parking is almost always available on Hinman Ave one-half block east, if the metered parking in front is full.
New Day Cafe is a new breakfast-all-day & lunch place just opened on Central Street east of Central Park Avenue. I understand that the folks that own the Bluefire Grill (burger & salad type bar/restaurant) on Central just west of Green Bay own the New Day as well. I should say that the Bluefire is not a favorite of mine, despite several attempts to like the place. The New Day seems pleasant (exposed brick, etc.) and the coffee was strong enough for me. I want to like it, because it is within walking distance of my home. But the prices seemed on par with Walker Bros. for lower quality, and the house-made corned beef hash was very disappointing (- chunks of previously frozen homefries browned and mixed with ground, salty industrial corned beef, no perceptible onion.) Not a great start, but I will give it another try, since Prairie Joe's is closed Sunday, and Walker Brothers is just mobbed.
Although I haven't been there at breakfast time, I believe that La Cazuela on Clark serves breakfast, but check to be sure.
Man : I can't understand how a poet like you can eat that stuff.
T. S. Eliot: Ah, but you're not a poet.