Ask and you shall receive...at least for Born in China and India populations by community area.
Downtown area has about 7000 people born in China now. That's an increase of nearly 3700 people since 2010. Now, if you add in Bridgeport, Armour Square, Brighton Park, McKinley Park, Douglas, Kenwood, and Hyde Park, then there are just over 30,000 people born in China living in that area. An increase of about 8000 people since 2010.
Now here's what is crazy - 375,000 people live in the area above meaning that 8% of every single person who lives in that area was born in China. Although Manhattan is 4X the population (and a little over 2X the born in China population), their percentage is 4.1%. That area of Chicago is nearly 2X more than Manhattan percentage wise. Queens, which is even bigger, is just over 7%. Of course, comparing a place of 375K to another one of 1.6 million and another of 2.1 million is weird but that is pretty crazy and way higher than I ever imagined. FYI, Manhattan's born in China population only increased about 4000 people from 2010 to 2016, but of course Queens increased over 28,000 in that time
Born in China, Change from 2010 to 2016:
1. Near West Side: +1406 people born in China
2. Armour Square: +1350
3. The Loop: +1063
4. Douglas: +816
5. Brighton Park: +629
6. Near South Side: +621
7. Bridgeport: +588
8. Near North Side: +579
9. Kenwood: +535
10. Hyde Park: +334
11. Archer Heights: +235
12. Lincoln Park: +189
13. New City (Back of the Yards): +187
14. Lake View: +164
15. Albany Park: +161
16. Norwood Park: +159
17. Lincoln Square: +124
18. Dunning: +122
19. West Elsdon: +119
20. West Town: +102
2016 By Total Number of People Born in China
1. Bridgeport: 8300 people born in China
2. Armour Square: 7567
3. Near West Side: 2609
4. Brighton Park: 2083
5. McKinley Park: 1949
6. Near North Side: 1655
7. The Loop: 1646
8. Douglas: 1222
9. Hyde Park: 1191
10. Near South Side: 1054
11. Lake View: 837
12. Kenwood: 746
13. West Ridge: 555
14. Edgewater: 543
15. Lincoln Park: 540
16. New City (Back of the Yards): 470
17. Albany Park: 405
18. Uptown: 392
19. Rogers Park 356
20. Lincoln Square: 277
Born in India, Change from 2010 to 2016:
1. Near North Side: +572 people born in India
2. Loop: +488
3. North Park: +469
4. Edgewater: +314
5. Near South Side: +304
6. Albany Park: +233
7. Douglas: +224
8. Rogers Park: +203
9. Near West Side: +186
10. Lincoln Park: +125
11. West Ridge: +121
12. North Center: +120
13. Lake View: +105
14. Austin: +82
15. Woodlawn: +80
16. Lower West Side: +78
17. Edison Park: +76
18. Montclare: +73
19. South Lawndale: +53
20. Hyde Park: +49
2016 By Total Number of People Born in India
1. West Ridge: 3437 people born in India
2. Near West Side: 1916
3. Near North Side: 1829
4. Albany Park: 1368
5. Edgewater: 1276
6. The Loop: 1204
7. Lake View: 1000
8. North Park: 970
9. Douglas: 618
10. Near South Side: 617
11. Lincoln Park: 463
12. Lincoln Square: 444
13. O'Hare: 432
14. Uptown: 413
15. Irving Park: 412
16. Rogers Park: 396
17. Hyde Park: 313
18. Forest Glen: 241
19. West Town: 233
20. North Center: 218
The downtown area added 1550 people born in India which is good though it still pales in comparison to what the Born in China population did especially in the greater area. I think a lot of the people born in India are probably moving to the suburbs. The total change in Born in India population for the city proper is +1300 or so while the Born in China is almost +9000.
As far as Mexican born population in the city goes, not good - the net all together is just under -17K people. With an overall increase in Mexican born population, then we could maybe figure that these people could be moving to the suburbs.
Here's a look at the top gainers from 2010-2016 for Mexico though:
1. Chicago Lawn: +1805 people born in Mexico
2. Garfield Ridge: +1300
3. Ashburn: +1032
4. West Elsdon: +976
5. West Lawn: +798
6. Portage Park: +730
7. Brighton Park: +644
8. Austin: +614
9. West Englewood: +464
10. Irving Park: +464
11. Edgewater: +291
12. North Lawndale: +272
13. Dunning: +230
14. Hyde Park: +183
15. O'Hare: +177
16. Englewood: +175
17. Edison Park: +110
18. Loop: +108
19. Jefferson Park: +98
20. Calumet Heights: +85
Unfortunately, we also have numbers like this:
* Lower West Side: -3845 people born in Mexico
* Logan Square: -2907
* South Lawndale: -2755
* West Ridge: -1038
* Albany Park: -1628
* East Side: -1484
* Rogers Park: -1463
* Uptown: -1327
* South Chicago: -1222
* Hermosa: -1028
* Avondale: -1023
* Gage Park: -907
* Lake View: -894
etc. The top 2 are probably gentrification, especially Logan Square. Might be able to say the same about Albany Park and Uptown in small ways and Lakeview too.