if you have a car, don't be afraid to look in the suburbs too. even if you have a job or school in the city, there's plenty of public transportation options to get downtown. i live in Naperville, and can get to the city under an hour on a good day. maybe a little over an hour during traffic. naperville, wheaton, arlington heights, palatine, downers grove, glen ellyn, oak brook, are some places to look to.
depending on your budget for living needs, you should look outside city limits too.
if you have a lot of stuff to transport, you can look into either renting a uhaul by yourself and make a couple trips over a week or two, or even look at a shipping company to pay them to transport it. you should be able to get quotes or rates online if you google moving companies. read reviews on yelp, angie's list, and others to find reputable companies with good reviews and recommendations.
figure out what your budget is on your income. ideally, you only should be spending no more than 30% on rent. if you are renting, you will also need renters insurance.