I've worked with several renters in Glenview in the past couple months, unfortunately I rarely see Glenview rental listings come on the mls at $1100 or less, and when they do come on, they have been in the unincorporated Glenview area.
Is there anything you are trying to be in close proximity to? Having pets definitely limits your possibilities further, so its good you mentioned you don't have any as that would be one of the questions I would normally ask.
Good Luck in your search :)
Paul Cionczyk| Coldwell Banker Residential Brokerage |Broker
312-433-9931 | PaulCionczyk.Broker@gmail.com |PaulCionczyk.com