Spiaggia, Piccolo Sogno, Coco Pazzo would be my top choices.

Spiaggia is head and shoulders the best, but you'll pay for it. Might also see the Obamas and other celebrities if they're in town. Jacket required and it's not strictly in River North (but very near).

I've also heard good things about Prosecco and Scoozi's. And Maggiano's is good if you're not looking for anything particularly fancy. All are in River North.