I would find out if your bank is one of the large national banks - as someone else mentioned if you bank with Bank of America, Wells Fargo, Chase, etc., you likely won't have to do anything. If not, then you will need to switch banks, but BEWARE, do NOT close your current account until you have a new account established. If you write a check from your current bank to your new bank the new bank could put up to a ten business day hold on your funds. Even if it's a cashiers check there's no guarantee a bank won't put a hold on that either for a new customer. Most important thing is to just plan ahead so you have access to your money and aren't stuck for days waiting for a bank hold to clear.
Go to your bank and ask them if they have any locations in Oklahoma City..........if they do - no problem.
If they don't - then you will need to find a new bank, open and account and then close the other one.
If you use a national bank like bank or america, wells fargo, etc, then you dont have to do anything. Your atm and checks and everything work just like they always did. No reason to do anything else, although you want to make sure there is an atm close to you or on your route, as you dont want to be running all around since time is money.
Close the one in IL and take the money and immediately open one in OK.