There are many dry cleaners in Evanston, but I go to Lake City Cleaners because they're open later than some of them, 6 or 7 p.m.
They also send coupons in the mail a lot of times. They're not cheap, but with the coupons, it makes it worth going. They have 89 cent men's shirt cleaning on Wednesdays also.
They do a good job, and have always been able to get something cleaned or altered for me in a really short amount of time, so if you need a job done ASAP... try them!