I don't know if it is still there, but when I used to work at one of the campus attractions, there was a hot-dog stand on the south side of the Field Museum that was excellent.
I ate at a hot dog stand at the NE corner of the Field property earlier this Summer - and the hot dog I bought and ate there was excellent; no need to venture away from the Museum property. For ice cream, other snacks/beverages - there's a larger concession stand (small house-like structure) on the E. side of the Museum property, sort of between the Field and the Shedd.
Here's a link to an earlier discussion where I posted a couple of pictures, including one of the hot dog from the cart I mention above:
http://lthforum.com/bb/viewtopic.php?t= ... ight=field