When you say "downtown", which part of downtown will you be in? The Loop (our commercial office district) or the "Mag Mile" of North Michigan Avenue (our luxury hotel and shopping district) or the nearby South Loop, West Loop, etc?
If I had to name one excellent restaurant in those two areas in the price range you mention, one that's open on Sundays, it would be
Atwood Cafe in the Loop for contemporary American, and
Cafe Spiaggia on the Mag Mile for Italian. Click on the name to see their website, which include menus with prices (note that Cafe Spiaggia's website also includes its far more expensive sister restaurant, Spiaggia, so don't confuse the two; click on "CAFE").
If you wanted to go more for the $15 entree rather than the $25 entree, I suggest going to one of the Greek restaurants in Greek Town just west of the Loop (e.g.
Santorini,
Greek Islands), or one of our places for Chicago-style deep-dish pizza (both
Giordano's, for double-crust "stuffed" pizza, and
Pizano's, for single-crust "pan" pizza, have locations in the Loop and near the Mag Mile).