Now, in terms of arancini, I love these, I am willing to bypass the 'frying' aspect because they're too damn good. Best I've had are the ones in Sicily, but that doesn't mean others can't come close.
First, in the NW burbs. A new place on Lake Street in Roselle (right by the corner of Roselle/Bloomingdale Road and Lake Street), Pizzeria Antiqua has them. From my 'contacts' by just eating around a lot, this guy appears to be the man in supplying the arancini to everyone else, including a lot of people who claim they make them themselves. The benefit of going to this place, they can fry them fresh for you (really can't compare this taste to heating it up later). It's right near me, so I really enjoy it. The location is kind of crappy, as it might be hard to miss, and you have to be going west on Lake Street to get in (after passing Roselle/Bloomingdale Road, or else you have to make a U-Turn if coming the other way). Looks kind of dinky, but the taste is worth it. I also like their Italian style pizzas and calzones.
One more place, Graziano's in Niles, with one exception. I had these here one night, and I thought they were amazing, closest I've had to Italy. They had like a creamy bechamel type sauce and cheese as the main ingredients, just like in Sicily (compared to the red sauce, peas, meat standard you'd normally find). Now, the exception, I got this is a 'nightly special' on the insert on the table. It's not a regular thing, it was listed as an appetizer (one order gets you about 4 small ones). I went on a Sat night a couple months ago, so just a heads up