I bet this is too late but hopefully this will help folks in the future . . .
There's a small little burger place on Adams between MIchigan Ave & Wabash called Patty's Burger. It's just burgers and fries but the few times I've been there I had a very good 40's style cheeseburger, that was just juicy/greasy enough but not too much so.
If you have kids and need something fast but you want eat a little better/more variety, Baci on Michigan Ave due west of the Bean has decent minestrone & pizzas and a wide variety of salads and sandwiches. The salad trio is nice if you want to take it away to "picnic" or eat after ice skating.
One place I have not been but colleagues speak highly of is the Pittsfield Cafe in the Pittsfield Building at 55 E Washington. Supposed old school charm, ancient waitresses, straightforward comfort food . . . haven't been but keep meaning to. I do not know if they are open on Sundays but they are on Saturdays.
hope this helps!
bjt
"eating is an agricultural act" wendell berry