At a $1000 budget, even if you are including having utilities included, you shouldn't have a problem.
For local apartments check this:
The Enterprise Newspaper Plainfield Illinois
I've used
Apartments for Rent and Homes for Rent although be aware that this is mostly corporate style large apartment complexes. Also you can enter any email address to register if you want to avoid junk mail.
I've also found that calling any local real estate office in the city you want to move to and telling them what you are looking for may lead to an apartment or they may refer you to another agency that deals with rentals.
Also a big help, not just for rentals, but for things to buy etc. is craigs list at
craigslist: chicago classifieds for jobs, apartments, personals, for sale, services, community, and events
If you've not heard of craigs list, you should check it out.
Good luck.
Welcome to Chicago.