Some shelters do neuter, you’ll still want a bunny-savvy vet. Call and don’t be afraid to ask how many they have performed on rabbits and if there is an exotics vet on duty that can do it. I have a list of questions to ask a vet and I think BinkyBunny has that list available too. As for the reliability/safety I cannot vouch as I have never used that venue but I know that there are some members here that work at shelters, maybe they’ll be able to help.
Here is a list of questions to ask a vet & after-care:
http://www.rabbit.org/faq/sections/spay-neuter.html#vet
List of Q’s to ask a vet:
http://www.rabbit.org/faq/sections/vet.html
This is a fairly new way of finding a vet as well through Goolgle:
http://www.vet.net/
Have you checked the HRS web site for vets in your area? http://www.hrschicago.org/articleslay1.html
You may also want to try the phone book and call for prices. I’m sorry I can’t help more. I’ll look around and see if I can find anything. If memory serves me correctly, there are some members here who live in the Chicago area and might be able to offer up more suggestions.