Here are the six examples found of the largest city in population of a particular state not being the core of the largest metropolitan area. Interestingly, all but one example come from the South. It is also interesting to note how close Memphis and Nashville are in city population – a virtual tie. Charleston and Huntington are in a tight race for first city of West Virginia too.
On the opposite end of the spectrum, Jacksonville and Houston are considerably larger than their nearest in-state rivals. However, Jacksonville falls into fourth for Florida metro areas while Houston continues to be a bridesmaid to Dallas-Fort Worth.
Population estimates from the Census Bureau for the cities are from 2013 and for the metro areas are from 2014.
CONNECTICUT
Largest city Largest metro
Bridgeport: 147,216 Hartford: 1,214,295
New Haven: 130,660 Bridgeport-Stamford: 945,438
Stamford: 126,456 New Haven: 861,277
Hartford: 125,017
FLORIDA
Largest city Largest metro
Jacksonville: 842,543 Miami- Fort Lauderdale-West Palm Beach: 5,929,819
Miami: 417,650 Tampa – St. Petersburg: 2,915,582
Tampa: 352,957 Orlando: 2,321,418
Orlando: 255,483 Jacksonville: 1,419,127
OHIO (thanks for the reminder, Jonathan)
Largest city Largest metro
Columbus: 822,553 Cincinnati: 2,149,449
Cleveland: 390,113 Cleveland: 2,063,598
Cincinnati: 297,517 Columbus: 1,994,536
TENNESSEE
Largest city Largest metro
Memphis: 653,450 Nashville-Murfreesboro: 1,792,649
Nashville: 634,464 Memphis: 1,343,230
TEXAS
Largest city Largest metro
Houston: 2,195,514 Dallas-Fort Worth: 6,954,330
San Antonio: 1,409,019 Houston: 6,490,180
Dallas: 1,257,676 San Antonio: 2,328,652
WEST VIRGINIA
Largest city Largest metro
Charleston: 50,821 Huntington-Ashland: 363,325
Huntington: 49,177 Charleston: 222,878
Sources: en.wkipedia.org and Census Bureau
problogic
Panethos 
The major Ohio cities represent an an interesting example of this. Columbus is far and away the largest in city population, but still lags Cleveland in metro population after recently passing Cincinnati.
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Good point and I feel dumb for not including that example. Will have to add. Thanks!
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I wonder what we are measuring here. It looks to me like we are measuring fragmentation. Cities are governmental units, metropolitan areas are economic units. They would diverge if the large metros tended to fragment more. It could also be that for particular reasons, a few cities were very aggressive in annexation and thus got a much larger share of the metro growth than their peers, even if the metro growth was smaller.
There are some interesting similar cases you did not note related to bi-state metros. Covington, KY is not the biggest city in KY, but I bet the Cinci metro is the biggest metro occupying a portion of Kentucky. The same would be true for West Memphis, AK. Also true for Council Bluffs, IA. Metropolitan areas as economic units often straddle state lines, which are arbitrary government units.
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