You’ll find Mexican stuff all over Chicago. Irving Park is something like 40% Mexican.
Pilsen is cheaper because it’s the South Side, and the South Side is not the trendy part of town. I live on the Southwest Side, in a predominantly Mexican and Polish working class neighborhood. It’s fairly inexpensive around here. You can find 2 bedrooms for under $1000 a month. You can buy a house for $150K.
Pilsen was hailed as the “next Wicker Park” in the mid-90s, when Wicker Park and Ukrainian Village became too expensive for the artist types. I never got the sense that it ever achieved quite that cachet–the North Side is still far more desirable for whatever reason, but it does appear to be continuing its gentrification. Pilsen is a diverse neighborhood and great value for what it offers. Not everyone is going to fall in love with it, but I think it’s great. It’s got a good mix of young arty types, neighborhood blue-collar family types, and white collar business professionals. Some people may try to tell you it’s “dangerous.” It’s an urban neighborhood, so you do need some situational awareness as in any other neighborhood, but it’s no worse than Logan Square or Uptown or any of a number of up-and-coming/up-and-gone neighborhoods.
Of the neighborhoods mentioned (Irving Park, Ravenswood, Pilsen), Pilsen would be the one I’d go for in terms of bang-for-buck, proximity to the city, and overall “stuff to do” in the neighborhood.
Other South Side neighborhoods worth looking at include Bridgeport and Hyde Park (University of Chicago area.) Maybe even McKinley Park. I personally like Hyde Park quite a bit, but I’m a sucker for university neighborhoods. It’s located right on the lake, you have many dining options (although most of them are just mediocre), a handful of bars (it doesn’t have the greatest nightlife, but Woodlawn Tap aka Jimmy’s and the Cove are both nice little dives.) Getting to downtown is best achieved via the Metra. Plus you can easily find one bedrooms at under a grand a month. Hell, you could probably find a studio for $700 or so.