I am moving to Illinois from another state as well! I was told to apply for licensure in Illinois. It is kind of a challenge in Illinois though.
This is how I did it:
I applied online first for the appropriate license. Then, I gave my school the ED-NUR form which you can print off from the internet as well. You also have to have your school send your official transcript to them after you graduate.
For the fingerprints - you'll have to contact the Illinois Department of Professional Regulation to have them send you an out-of-state fingerprint card. Then you have to go a local police authority, get ink fingerprints. Then, you have to find a place in IL that will process your fingerprint card. The directions for this will come with the out-of-state fingerprint card. Then, you submit the FP-NUR to Illinois as well - it's a form stating you completed this fingerprinting process.
The fingerprinting part is the worst - especially if you are out of state. And, when you call the IL dept of professional regulation, be ready for it to be busy ALOT. I usually try to call in the morning and just call repeatedly, you'll get through eventually. Then, you'll need some time to be on hold - I've called about 3 times and never been on hold for more than about 20 minutes..so it's not too bad.
This sounds awful I know - but you can do it! It's all available online. I spent a long time trying to get it all right - so if you have any other questions once you get started I might be able to help. Good luck!