If you will be living alone, and are a pretty simple person, you may consider some of the small office spaces right in the Financial District. You'll need the bathroom key. And have to lie about your purpose in renting the space, but it's cheaper than anywhere else within miles.
Otherwise, decide if you are going to rent or buy.
There are plenty of affordable rentals in the Gold Coast, where you could walk during the summer to the financial district. If you are buying, there are very affordable older condos in Lincoln Park. And if you want a house, you should check out Bridgeport or Pilsen, otherwise go further north to Portage Park or Jefferson Park. And then, you may like a multi-unit (multi family) like a two flat or a three flat. That will open up more areas for you.
Buy High. Sell Low.