The capital of Illinois is Springfield (not Chicago), the capital of NY is Albany (not NYC), the capital of Washington is Olympia (not Seattle) and the capital of California is Sacramento while it has such amazing cities. Springfield and Albany are almost villages and yet they hare capitals.
There are some that I think I understand. For example, Baton Rouge or Richmond might have been financial powerhouses back in the day but what's the reason behind such odd choices for NY, Florida, Illinois etc?
Mentioning previous answers is not intended to discourage further questions or discussion.
Edit: I should add caveats on a lot of these. There were a lot of replies -- this is a popular question. Few of the replies listed sources, and some in the threads were a couple of sentences that might have been hearsay. So these postings linked below should be read carefully and critically.
From scanning the answers, there's no sui generis answer. MrDowntown points out, "First, in 17 states, the capital is the largest city." Sometimes it was a compromise caused by the struggle of two more-important cities. Sometimes it used to be much larger in percentage terms and close to the average population center of the state (NV, CA, IA, WI). Sometimes it was protection from invaders (VA, SC, Canada, an Atlantic Canadian province). Sometimes there was chicanery (ID, TX). Sometimes it was geographic (IN). Sometimes it was something else (KY: $). And I'm probably missing some.
Why are US state capitals often not the largest or most economically "important" city in the state? at https://www.reddit.com/r/AskHistorians/comments/5o3k7v/why_are_us_state_capitals_often_not_the_largest/ : lively discussion and examples by a number of people, including /u/justanothercap (CA), /u/Eternally65 (VT), /u/DrewInBalto (MD), Chernograd (NV), lilkovakova (PA, TX), Gorrest-Fump (VA, SC), llcucf80 (FL), SovietBozo (KY).
In Canada, provincial capitals are often also the 1st or 2nd largest cities in the province, but in the USA, state capitals are often far smaller than the most populous city in the state. Is there a historically interesting explanation of this? at https://www.reddit.com/r/AskHistorians/comments/433nk2/in_canada_provincial_capitals_are_often_also_the/ : LifeMadeSimple (CT), IAmVeryAttractive (CT), jackanapes8 (MI), EagleFly_5 (), P-Rickles (OH), shwag945 (CA), JohnHenryAaron (NV), grantimatter (FL), PoetryStud (SC), Machipongo (IL), sleepyintoronto (), GeeWarthog (TX), CantabKBH (New England), another SC, another TX, another FL, Stantron (WA), thedankbank1021 (KS),
Why isn't NYC the capital of New York? at https://www.reddit.com/r/AskHistorians/comments/3mitxa/why_isnt_nyc_the_capital_of_new_york/ : discovering_NYC (NY)
Is there a historical reason why state capitals in the US are generally not the most populace? at https://www.reddit.com/r/AskHistorians/comments/2gvngf/is_there_a_historical_reason_why_state_capitals/ : rjw55 (IA, WI)
Why are most (maybe all?) State Capitals in some of the smallest cities of their states? at https://www.reddit.com/r/AskHistorians/comments/23zjfq/why_are_most_maybe_all_state_capitals_in_some_of/ : MrDowntown points out "First, in 17 states, the capital is the largest city.", and then goes over retreaded territory.
How were the United States' capitals picked? Did they naturally arise from large cities, or was there some sort of deliberation? If so, what is taken into consideration? at https://www.reddit.com/r/AskHistorians/comments/1040ix/how_were_the_united_states_capitals_picked_did/ : I'm getting tired, so I'll only mention new states: The_Alaskan (AK), CrossyNZ (New Zealand ... I've skipped over other discussions of Canadian capitals &c), ghosttrainhobo (IN), deleted (Australia), Sherm (OR), username_redacted (ID), rj22497 (GA), DV1312 (Germany), Six_of_Spades (more MI), eonge (WA).
And damme if I'm going to post enough replies to /u everyone mentioned here.