What do you mean by "late afternoon"? The reason I ask is, some places stay open all afternoon, while others close for lunch (typically around 2:00) and open for dinner (typically around 5:00). For example, Prairie Grass Cafe does that; between 2 and 5, they offer light fare in the bar, which might not be what you're looking for. OTOH if you're planning to dine at 5 pm, you can pretty much go anywhere.
If you're not dining till 5:00 or later, I think Prairie Grass Cafe is appropriate for what you're looking for, with American comfort food, and an atmosphere suitable for kids. I've been to Miramar several times, and although the atmosphere does connote a mid-20th-century Havana, I've found the food just okay, and all in all, not particularly alluring in any way.
How about the good steakhouses? They're suitable for kids, and most are open all afternoon, too. You've got Wildfire in Lincolnshire (open all afternoon) and Pete Miller's in Wheeling (opens 4:30). You're probably already familiar with the Tavern in Libertville (opens 5:00), which I think is pretty good too.