A pretty typical pattern for me, especially if I'm arriving late or departing early by air, is to book the first (or last) night's stay at the airport hotel. Conceivably that could happen twice if you're doing both (arriving late and departing early). That tends to break up one continuous hotel stay.

You may also be able to store luggage for the day (or two) that you're not at a particular property (but are returning). That can ease the moving in/moving out trauma. Here's an example:

Night 1: Stay at Hilton O'Hare. Store excess luggage.
Night 2: Stay at one of the downtown Chicago Hilton properties. Overnight bag only.
Night 3: Stay at the Hilton O'Hare. Luggage delivered to room.