As far as programs go, look into Illinois Masonic Hospital. They have an RN residency program. Heard it is great, though I did not apply for it. They are part of the advocate system. They will send you info.
I graduated last may. Some students started applying in April, got hired, and started in June or July. (license pending.) Some applied after they took the nclex. It is all up to you. Most hospitals accept license pending nurses. Most accept ADN and any new grads with open arms.
Starting pay.... i see from 22-24 starting days, with a few bucks differentials for evenings, nights and weekends. I saw one place at 23.50 days, 2 dollar night, plus 2 dollar weekend differentials. (i dont work yet bc of injury-so i cannot tell you much else)
Cost of living here I heard is expensive. I live here, so to me it is normal!!
If you live in one of Chicago's fabulous neighborhoods (wrigleyville, lakeview, lincoln park, etc) it is expensive, jam packed, and parking is hell--though there is lottsss going on.
If you live in the burbs, or northwest side of the city, its better (at least thats what i think). The city is huge and has lots of opportunities. Each area is different. Go to chicago's craigslist.com, also... you can meet some cool people from chicago, look at apt rentals, etc.
Good luck. Chicago is aweeessommmmeeeee.