No doubt Stanford is an extraordinary university, but comparing Chicago with Palo Alto is simply nonsense, weather included. You have to deal with winter weather only two months a year since the students leave campus in the first week of December. The rest of the year the weather is awesome, besides January and February, and, in my opinion, nothing compares to having four seasons.
Also, the cultural life, internships, and job opportunities in Chicago can be compared only to NYC’s, and that means a lot to many prospective students.