The answer to the question is hiding inside the question: Chicago is what attracted/attracts so many hispanics to the Chicago area. It's a big city forchristssake.
There are not nearly as many Mexicans in New York City or Philadelphia. Chicago really stands out in terms of specifically Mexican population outside the southwest.
No where in the midwest really has more Caribbean Hispanics than Mexicans, I'm pretty sure even Cleveland hispanics are mostly mexicans.
But for what its worth Chicago does have a large Puerto Rican population. I believe Luis Gutiérrez district is split between a Puerto Rican section and a Mexican section and he is puerto rican.