my best advice to you... if you have a friend in chicago, ask them to help you find an apartment.
it will be expensive to rent a furnished apartment for such a short time but renting an apartment will be cheaper than using a hotel. also, renting an apartment allows you to live in a neighborhood that will be more comfortable than living in a hotel. corporate housing companies are also great, but often more expensive than hotels.
chicago is a big city with much to explore, you will love it here!