Be careful...
Jumper8,
Jackolantern has a valid point. To us casual readers, it does seem from your description that you are interpreting "residency" in conveniently different ways depending on whether (a) it is for the purpose of citizenship or (b) Illinois in-state tuition. You cannot be a resident of two states simultaneously. And you should be careful, because sending a mixed signal to the IO could complicate your case.
I would guess that in a large number of the cases, establishing residency is a clear cut issue. People stay in one jurisdiction or if they move during the process, the move is straightforward and their file is transferred to another jurisdiction. In these cases, the driver's license is sufficient to establish residency. You will note that the interview letter specifically asks you to bring a state id in _addition_ to your passport, green card and social security card. One reasoning could be that the USCIS wants to use it as a secondary id, another could be that they will use it to confirm residency. Note that the interview letter does not ask for any specific residency proof, so personally I would vote for the later.
Now there are probably a smaller number of cases where residency is not clear cut. People often work in one/multiple states but live in another. Many older people split time between Florida and another "home" state. Students go to school in a state different from their parents or "home". The USCIS field manual that boatbod quoted tries to give some directions on how to deal with such cases, but as the guide itself says, its in the hands of the IO. The law requires them to check that the application was sent to the right district. (this residency requirement does not make sense to me , but nothing we can do about it, its the law).
Please note that I am not a lawyer and what I write below is based on personal reading as well as the experience of a friend who has a somewhat similar situation. (He used prior tax returns to prove residency).
In your case, if you had applied using IL as your home state, things would have been very simple. You are a student in that state with a local home. Now that you have applied in a different state and have been living there, it is in your interest to confirm residency in that state, without showing any ties to IL. If you go strictly by the field guide, you can prove that by showing a local in-state license or with tax returns. Perhaps a lease may be acceptable as supporting proof too, but nothing stops a person from renting apartments in multiple states, so in my opinion that is not sufficient to prove residency. If you are a student supported by parents living in that state, that makes you eligible too.
Note that once you get a new license as you are planning, you cannot be an IL resident. The DMV will take away your old license. Even if they give it back, it will be canceled electronically. Depending on how strictly your school verifies residency when you go back, they could say you gave up IL residency and must now wait for a certain period before you can claim in-state tuition. For instance, in Florida, you cannot move to the state for the express purpose of education and claim in-state tuition. You have to be resident prior to that or have to wait for a year.
Sorry, its a long mail but the summary is that you should provide a clear cut proof of residency to the IO if the issue comes up. As Jackolantern correctly pointed out, if you go back and forth and want it both ways, it will not look good.
Regards.