For eaters with limited palates... I would also add to the list BBQ and fried chicken spots, in addition to the pizza, burgers, etc:
Hill Country BBQ
Hill Country Chicken
Blue Smoke
Clinton St Baking Company - especially for breakfast!
Westville - American comfort food
Otto - pizzas, pastas, gelato
Meatball Shop
City Bakery - high quality breakfast buffet bar, some of the best French toast ever
Dependent upon what they like / don't like... and/or how much you feel like pushing the envelope:
You could hit up some classics like Russ & Daughters, Katz's Deli, Papaya King, William Greenberg's for black and whites, Junior's for cheesecake, egg creams from Gem Spa or Ray's, Pickle Guys.
Am guessing Halal Guys is a bit too adventurous? If you want to go to Halal Guys, check out their Facebook Page and make sure it's not one of the imposters.
Would they try Korean fried chicken from Bonchon?
What about Korean BBQ at Madangsui?
For fun, deep fried (non-breaded) hot dogs with creative toppings, Crif Dogs now also has a West Village location in addition to the East Village one (and a Brooklyn one).
If the menu at Shopsin's too intimidating? You can get something really unique and adventurous and they could stick to the "normal" stuff?
Some of my other favorite spots who serve weekday breakfast are Joseph Leonard, Balthazar, Lafayette, and The Breslin. Take a look at the menus - there are some creative dishes on them, but some are "safer" than others.
If hanging around Midtown / 5th Ave anyway, Rockefeller Center has Jacques Torres, Bouchon Bakery, and Magnolia Bakery. Momofuku Milk Bar isn't too far either. And you could stop by Burger Joint in the Parker Meridian for the "hidden" burger joint behind the curtain in a fancy hotel.
John's Pizza in Times Square is not that great and pales in comparison to the one on Bleecker St. If you're OK with Naples style, try Don Antonio By Starita. Or PizzArte. If downtown, near the Bleecker St John's, and it's nice out, do takeout so you can skip the line. Call ahead, get a pie, max 1-2 toppings (I like their green bell peppers), and eat it outside at Father Demo Square or Washington Sq Park.
Grimaldi's has gone way down hill in the last several years. However, Patsy Grimaldi (who sold Grimaldi's back in the day), has actually come back out of retirement and started up Juliana's, practically next door to Grimaldi's.