E.R.
Normally someone ELSE would throw your shower- a mom or sister or girlfriend, whoever. Is there anyone else that could have it at their place? Other women, especially ones who have had babies are usually really helpful and supportive at this time and you might be surprised who might volunteer to help out if they just know that you need it!
You totally don't need the stress of trying to do this alone- or the expense of going somewhere. If it would just be a small group of friends, how about a friendly coffeehouse like Uncommon Grounds on the northside or the Buzz Cafe in Oak Park? Both places are VERY kid-friendly and then your shower invites can just order coffee or whatever they would prefer. Call ahead and ask if it would be all right for you to just bring a cake in with you to celebrate.
The suggestion below about being a church member is also a good one! Part of being at a church is that you have a great supportive community (one that often includes daycares, good babysitter contacts and other mamas with advice and hand-me-downs and other practical help!) and I am sure if you are involved with any sort of church, they would let you have your shower there if you just talk to the minister or rabbi or whatever and explain your situation.
Remember, this is YOUR event for you and your baby! Your friends and co workers and family WANT to help and support you at this time- not to stress you out and make you spend money you don't have on entertaining them! Talk to a few friends and see if someone would host at their place- or go public and just let a few close friends know it will be a 'get your own coffee' kind of get together and ask if they could just pass the word around, so you don't have to.
Above all, don't stress out and don't be embarrassed. What is important is that you welcome a happy, healthy baby and have the things you need to do that! Your friends will understand that and help you with it! Good luck- it will all be fine!!