The Northern Illinois market is extremely tight for new grads. If you don't already have family or other very influential people you know well, employed at hospitals you really will have a hard time.
Illinois has about 5600 newly licensed RNs each year. There is not even a fraction of jobs available for them. The hospitals who still have "residency" programs are few, and those often fill with those that are connected, or with nurses from BSN programs that the hospital has a history of preferring. This is not to say you absolutely won't be considered.
There are a lot of Home health companies in Illinois who take any breathing body. But beware, there will be no clinical infrastructure, and you will not receive any real training. These are often just somebody who manages to get a loan to buy EMR and some laptops and knows that it's the nurses he hires who will take all responsibility for care. Very dangerous with the acuity level of patients being discharge home these days. Very little chance you will be able to obtain any other job after employment with these companies. No year or two, then being considered for a hospital job being common. The hospitals have their own home health and those require hospital med/surg experience at minimum to qualify, and they do not consider your experience "real experience".