I don't think there's a comprehensive post on getting to the main areas by public transportation, so here's a stab at one. Access to food neighborhoods from downtown (presumes you get hold of a CTA map as soon as you get here):
Pilsen, the northernmost south side Mexican neighborhood (that makes sense to a Chicagoan, trust me), is a fairly short cab ride away or accessible from the 18th street stop on the new Pink line (does that mean the old Blue line no longer goes there? The Pink line is a new thing, so I'm not positive how all that works). The 18th street stop, anyway, is at 18th and Ashland, most of the strip is on 18th east of that point (e.g., Bombon, Nuevo Leon, etc.)
Chinatown is also a fairly short cab ride away from downtown, or you can ride the Red line south to the Cermak-Chinatown stop. Chinatown really has two sections-- the old, somewhat touristy but still lively Chinatown is on Wentworth starting at Cermak and going south, the Chinatown mall (which has a more modern-Beijing feel, minus 10 million people and bicycles) is the structure west of the subway station with a plaza in the middle and the backs of businesses facing the outside. Wentworth and that area has places like Little Three Happiness, Moon Palace, Penang, etc.; the mall has places like Lao Sze Chuan, Spring World, Shui Wah for dim sum, etc.
There's also another
"Chinatown," best known for Vietnamese restaurants like Tank Noodle and Hai Yen and anything starting with "Pho," up on the north side around
Argyle Street. The Argyle stop on the northbound Red Line is the easiest way to get there.
A lot of good
Mexican is in Logan Square (though it's gentrifying), Humboldt Square, etc. on the near northwest side. There's also some Polish in that area. I don't think they're very walkable areas though-- I don't mean you can't or they're notably unsafe, but there's a lot of walking between one point of interest and the next most of the time-- so you'd need to have a specific destination in mind and figure out how to get there via CTA (probably train and bus in combination).
The best
Thai food is mostly clustered around, oddly enough, a rapidly yuppifying old German neighborhood.
Lincoln Square is losing its old flavor quickly but is still charming to walk around, and then you can easily walk to Spoon Thai or Rosded, or walk/hop a bus about a mile south on Western to Sticky Rice. Take the Brown Line to the Western stop and you'll be right there.
Devon, the
Indian strip that eventually turns Russian Jewish, is one of the most fascinating places for a visitor to visit in my book, not to mention all the best Indian and Pakistani restaurants in town (search for Khan BBQ, Indian Garden, Udupi Palace, Hyderabad House, Usmania, Sabri Nehari, etc. etc.). Unfortunately it's not the most convenient to get to by CTA. You could take the Brown Line to Western again, then catch a northbound 49B (be sure it has the B, other 49s don't go all the way to Devon), or take the Red Line to Loyola and catch a 155 which will loop around onto Devon and take you the mile or two to where the strip actually starts (a few blocks east of Western, the continuing West to around Kedzie).