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"I have tried to add New York and Chicago together but it is too expensive with the connecting flights."
Book an open-jaw ticket from your originating city to ORD, with a return flight from JFK or EWR. Book the flight from Chicago to New York separately. (Check southwest.com for flights on Southwest Airlines from MDW (Chicago Midway,
not Chicago O'Hare) to LGA or EWR.) Or, if you'd like to visit a third city on your trip, check Southwest's fares from MDW to PHL; you can then take Megabus from Philadelphia to NYC -- often for under $10 USD if you book far enough in advance.
Check travelzoo.com for hotel deals in all three cities.