I know golfsmith allows you to demo rackets but it's $10 each time you do it (you get a $10 store credit for a racket purchase in return). This is pretty pricey compared to say tennisexpress.com where you can check out 4 rackets at a time for a max charge of $15-$16. (which covers shipping there and back). The shop I used to demo rackets at closed down (chicago golf and tennis near belmont/kimball) don't know of any other place that demos rackets unless of course you belong or know somebody who belongs to a club (like Midtown).
You may want to contact 40-love Tennis Pro Shop - located at McFetridge Tennis Center. I'm sure you could make arrangements to reserve a court and have the demo racquets made available.
Your Advantage will let you demo up to three racquets at a time for a period of 2-3 months. There is a $25 fee that is credited towards stringing should you decide to purchase.
You might also want to try Tennis on the Lake Sporting Goods. I am not familiar with their selection or demo program but it may be similar to your advantage.
Please tell them you were referred by Chicago Tennis Collective. Below is a link to all the Chicago-land pro shops, including address and phone numbers. Let us know how it works out and what you decide to buy.
I did not mention Golfsmith because I don't think they have nearly the selection or expertise advise you will get at 40-love, your Advantage or Tennis on the Lake. The prior three are tennis specialists.