Uuugh. O'Hare. Well... if you're one that can stomach BAD traffic, you can certainly ride in from the airport hotels... but it's very specific. You will have to take Bryn Mawr Road west. You can dead end that road into Higgens Road a couple of miles down, then take Higgens Road west until you get to where it dead ends into Milwaukee Avenue. You're going to continue south and east (the road runs diagonally south but heads east also) all the way to Irving Park Road. From there, you'll head directly east on Irving Park Road until you hit a good street like 1) Elston (wich runs south and west, then dead ends into Milwaukee Ave again, then you would jump Milwaukee for a block and turn east on Chicago, and head east until you hit downtown), or you could 2) take Irving Park Road to a better street like Lincoln, then turn right at the Lincoln-Damen-Irving Park Road intersection and head south on Lincoln back to the city (very bike friendly street). Lincoln also runs diagonally and dead ends diagonally into Clark and Wells. I like to take Clark, which is a one way street heading south. But if I want to stop along the way and enjoy the riding a bit more, I'll head south on Wells. If you're in a hurry, take Clark.
From the get go, if you stay on Milwaukee and just take it all the way south and east, it will dead end into Kinzie, which is right downtown. I just hate taking Milwaukee because the street is so bad with so many potholes that you will end up feeling like you were pimp slapped about a thousand times and so will your bike! It's a great road because it's so convenient, but the condition of the road is just horrific.
If you're looking for the easy fast way to get into town, if you wait until after 9am, you can sling your bike on the blue line train and take the train headed back to the Loop. I think your stop should be the Cumberland stop, which is easy enough to get to from the airport hotels.
The ride from the airport hotels can be aggrevating at times, and you should have front and back lights. There's a section of road where there aren't a lot of lights, and it runs along some woods and it's twisty. A car coming from behind at a high speed would be surprised to see you, so be careful. I've taken that route a bunch of times, and I've never seen anyone else on a bike. There aren't sidewalks to jump and there's no shoulder either. But that only goes for a few miles at best, and then after that, it's just bad traffic, that's all. There's a Dairy Queen you can stop at that's closer to the airport than downtown, and usually, when I do a round trip, I'll reward myself with a stop at the Diary Queen for a soft serve. It helps to calm my nerves and prepare me for the trip back downtown!