Does Chicago have good New Mexican places? There are cities with great ethnic food places and cities with none. Pretty sure NYC, for example, has a reputation as a city without much in the way of Mexican cuisine.
Popping in to say Chicago has shittons of Mexicans. I'm one of them, or at least half of one. I don't know specifically about "New Mexican" or "Tex-Mex" cuisine (my family regards Tex-Mex with scorn, never had it myself), as the food I regard as Mexican food is either common throughout Mexico or found particularly in Nuevo León and that sort of region. But there are multiple neighborhoods with significant Mexican communities, and plenty of places to find that sort of food to dine on or make yourself. Chicago is one of the largest Mexican communities in the United States.
Chicago is also the biggest Polish community outside of Warsaw, so if anybody wants Polish food or pastries there is plenty of that to be had. Other significant ethnic (and thus ethnic food) contingents are Greek, Italian, German, Indian, Chinese, Puerto Rican, and a smattering of Eastern Europeans. Lithuania and Ukraine I know for sure but I know plenty of people of Romanian descent. I just don't know where the major Romanian population center in Chicago might be.