Straight Shot - A Day and a Half
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This is really a very straightforward drive. You get on I-80 in southern Chicago, and you don't get off it until you ready to roll into NYC and I-80 terminates at I-95. The easiest route from that junction in Northern NJ (at least in terms of having to remember it, so you can concentrate on the traffic, is I-95 (north) to I-295 south and the Throgs Neck Bridge. then either stay on I-295 or take the Cross Island Parkway depending on exactly where you're going in Floral Park. This is about a day and a half drive total, which should let you drive through New York during mid-day rather than rush hour, Trying to cover the entire 800+ miles in a single day is NOT recommended.
Personally, I would try for a very 'early to bed, early to rise' departure, so that you can hit the road before 6:00 AM and get out of Chicago before the worst of rush hour. Then plan to pull up in mid afternoon in northern Pennsylvania along I-80 somewhere (very roughly in the Williamsport area), take an evening stroll, get a good night's sleep, and be ready to head for the big city fairly early in the morning, aiming to hit the George Washington Bridge sometime around mid-morning, say 10:00 AM, so that you're with your family for lunch.
As for tolls, you can expect to pay roughly $4.00 for the Indiana Toll Road and $15 for the Ohio Turnpike. I believe that the George Washington Bridge will hit you for another $12 as you enter NYC, but it's free to leave. The toll on the Tri State Tollway will depend on exactly where you're coming from, but I suspect you're more familiar with it's rates than I am in any event.
AZBuck