Okay, using As Above So Below's great work, I took a look at population diversity and ranked the groups by pop. density for the UAs with 3M+ population.
The highest population density of any of the largest UAs is Whites in DC, followed by Hispanics in LA, and Whites in NY.
GROUP-URBAN AREA-GROUP PER SQ MILE:
WHITE-WASHINGTON: 3,824
HISPANIC-LOS ANGELES: 3,329
WHITE-NEW YORK: 2,373
HISPANIC-MIAMI: 2,247
ASIAN-SAN FRANCISCO: 2,239
WHITE-SAN FRANCISCO: 2,185
WHITE-SEATTLE: 1,990
WHITE-PHOENIX: 1,899
WHITE-LOS ANGELES: 1,795
WHITE-SAN DIEGO: 1,792
WHITE-CHICAGO: 1,702
WHITE-DETROIT: 1,694
WHITE-PHILADELPHIA: 1,641
WHITE-BOSTON: 1,532
HISPANIC-SAN DIEGO: 1,497
HISPANIC-SAN FRANCISCO: 1,456
HISPANIC-NEW YORK: 1,427
HISPANIC-HOUSTON: 1,411
ASIAN-LOS ANGELES: 1,385
WHITE-MIAMI: 1,348
WHITE-DALLAS: 1,251
HISPANIC: PHOENIX 1,136
BLACK: WASHINGTON 1,111
BLACK-MIAMI: 1,106
BLACK-NEW YORK: 1,093
HISPANIC-DALLAS: 1,079
WHITE-HOUSTON: 984
HISPANIC-CHICAGO: 843
BLACK-ATLANTA: 779
WHITE-ATLANTA: 777
BLACK-DETROIT: 753
ASIAN-NEW YORK: 733
ASIAN-SEATTLE: 726
HISPANIC-WASHINGTON: 706
BLACK-HOUSTON: 700
BLACK-PHILADELPHIA: 678
BLACK-DALLAS 668
BLACK-CHICAGO: 664
ASIAN-SAN DIEGO: 655
BLACK-SAN FRANCISCO: 634
BLACK-LOS ANGELES: 549
ASIAN-WASHINGTON: 528
HISPANIC-SEATTLE: 390
ASIAN-HOUSTON: 351
BLACK-SEATTLE: 323
HISPANIC-BOSTON: 309
HISPANIC-PHILADELPHIA: 307
ASIAN-CHICAGO: 305
BLACK-SAN DIEGO: 289
BLACK-BOSTON: 273
BLACK-PHOENIX: 256
ASIAN-DALLAS: 269
ASIAN-BOSTON: 249
HISPANIC-ATLANTA: 240
ASIAN-PHILADELPHIA: 226
ASIAN-PHOENIX: 212
ASIAN-DETROIT: 181
ASIAN-ATLANTA: 166
ASIAN-MIAMI: 159
HISPANIC-DETROIT: 146
Broken down by Urban Area:
New York City - 19,182,900 - 3,450 sq miles
White: 8,187,382 - 42.7% - 2,373 ppsm
Hispanic: 4,924,876 - 25.7% - 1,427 ppsm
Black: 3,771,008 - 19.7% - 1,093 ppsm
Asian: 2,532,350 - 13.2% - 733 ppsm
Los Angeles - 12,257,919 - 1,736 sq miles
Hispanic: 5,780,948 - 47.2% - 3,329 ppsm
White: 3,117,090 - 25.4% - 1,795 ppsm
Asian: 2,405,379 - 19.6% - 1,385 ppsm
Black: 954,238 - 7.8% - 549 ppsm
Chicago - 8,636,076 - 2,442 sq miles
White: 4,157,738 - 48.1% - 1,702 ppsm
Hispanic: 2,059,621 - 23.8% - 843 ppsm
Black: 1,622,424 - 18.8% - 664 ppsm
Asian: 745,873 - 8.6% - 305 ppsm
Miami/Fort Lauderdale - 6,001,189 - 1,238 sq miles
Hispanic: 2,782,465 - 46.4% - 2,247 ppsm
White: 1,669,455 - 27.8% - 1,348 ppsm
Black: 1,370,421 - 22.8% - 1,106 ppsm
Asian: 198,041 - 3.3% - 159 ppsm
Dallas/Fort Worth - 5,901,118 - 1,779 sq miles
White: 2,226,762 - 37.7% - 1,251 ppsm
Hispanic: 1,920,056 - 32.5% - 1,079 ppsm
Black: 1,190,589 - 20.2% - 668 ppsm
Asian: 539,128 - 9.1% - 296 ppsm
Houston - 5,721,108 - 1,660 sq miles
Hispanic: 2,343,850 - 41.8% - 1,411 ppsm
White: 1,635,259 - 28.6% - 984 ppsm
Black: 1,162,255 - 20.3% - 700 ppsm
Asian: 584,602 - 10.2% - 351 ppsm
Philadelphia - 5,672,800 - 1,981 sq miles
White: 3,252,602 - 57.3% - 1,641 ppsm
Black: 1,345,125 - 23.7% - 678 ppsm
Hispanic: 609,374 - 307 ppsm
Asian: 449,523 - 7.9% - 226 ppsm
Atlanta - 5,225,579 - 2,645 sq miles
Black: 2,063,341 - 39.5% - 779 ppsm
White: 2,056,644 - 39.4% - 777 ppsm
Hispanic: 635,020 - 12.2% - 240 ppsm
Asian: 440,405 - 8.4% - 166 ppsm
Washington DC - 5,047,533 - 1,321 sq miles
White: 1,930,742 - 38.3% - 3,824 ppsm
Black: 1,468,364 - 29.1% - 1,111 ppsm
Hispanic: 933,750 - 18.5% - 706 ppsm
Asian: 724,678 - 14.4% - 528 ppsm
Boston - 4,490,042 - 1,873 sq miles
White: 2,871,254 - 63.9% - 1,532 ppsm
Hispanic: 579,986 - 12.9% - 309 ppsm
Black: 515,935 - 11.5% - 273 ppsm
Asian: 468,409 - 10.4% - 249 ppsm
Phoenix - 4,120,530 - 1,146 sq miles
White: 2,177,964 - 52.9% - 1,899 ppsm
Hispanic: 1,303,698 - 31.6% - 1,136 ppsm
Black: 294,906 - 7.2% - 256 ppsm
Asian: 243,757 - 5.9% - 212 ppsm
Detroit - 3,773,566 - 1,337 sq miles
White: 2,266,223 - 60.1% - 1,694 ppsm
Black: 1,008,871 - 26.7% - 753 ppsm
Asian: 242,044 - 6.4% - 181 ppsm
Hispanic: 196,064 - 5.2% - 146 ppsm
Seattle - 3,560,825 - 1,010 sq miles
White: 2,001,696 - 56.2% - 1,990 ppsm
Asian: 733,413 - 20.6% - 726 ppsm
Hispanic: 394,023 - 11.1% - 390 ppsm
Black: 327,155 - 9.2% - 323 ppsm
San Francisco - 3,440,874 - 523 sq miles
Asian: 1,171,054 - 34.0% - 2,239 ppsm
White: 1,143,327 - 33.2% - 2,185 ppsm
Hispanic: 762,947 - 22.2% - 1,456 ppsm
Black: 332,417 - 9.7% - 634 ppsm
San Diego - 3,120,959 - 732 sq miles
White: 1,312,969 - 42.1% - 1,792 ppsm
Hispanic: 1,096,175 - 35.1% - 1,497 ppsm
Asian: 480,415 - 15.4% - 655 ppsm
Black: 212,854 - 6.8% - 289 ppsm