My SO and I are also from Chicago and traveled to MEX for his birthday in February. We stayed in a luxury hotel in Polanco area, and went all over the city (in a hotel-provided car and sometimes cabs, but never in a VW cab). We felt completely safe, and never felt otherwise. We had our hotel send a car for us to the airport and back. The restaurants and nightlife are fabulous, we actually loved our time so much that we are going back for my Birthday this September.

Pay attention to everything, like in any other city, and try to use either hotel cars or cabs called by restaurants or bars, but to be honest, I felt safer there than in many US cities. Truly a fantastic place!