Some that I find particularly good and bad.
First, the good:
New York is my favorite. It just seems not very capitoly.
Hawaii's seems especially appropriate for Hawaii, given the strong Asian influences there.
I also love Illinois' state capitol building. It's got that intimidating Victorian look to it.
And Louisiana... for being so reflective of the essence of Louisiana politics: "Mah dick is bigguh than your dick." Must've been good old boy you scratch my back I scratch your back make-work for the depression (built 1930-1932). Really though... of all the states in the south, in the country even... has culture like Louisiana has culture. It's one area of the country where I could rattle off a list of uniquely "American" things that make American culture neat.
My least favorites:
Florida: The new building is kinda nice in that it followed the form of traditional capitol buildings but used modernist crisp, clean, straight lines. But the way they kind of enveloped the old building...
Alaska: Let's face it. The Capital city of Alaska is probably the most beautiful capital city in the U.S.
So it would be silly to try and make a building a focal point with surroundings like that. But the capitol doesn't even really stand out from the surrounding buildings... let alone from those surroundings.
Minnesota's capitol is pretty run of the mill... but the civic planners in St. Paul did a nice job of showing you exactly how big the separation of church and state should be
I believe the tippy top of the Cathedral is just a tick higher than the capitol building as a snub by the local clergy. Our state constitution does go out of its way to tell the church to keep out.