State capitols with NO Amtrak service:
Helena, Montana
Carson, City Nevada - No rail service after the Virginia and Truckee was torn up in the 1950's (except museum stuff)
Cheyenne, Wyoming - was served (kinda) by the Pioneer
Bismark, North Dakota
Pierre, South Dakota
Des Moines, Iowa
Frankfort, Kentucky
Nashville, Tennesee
Annapolis, Maryland
Tallahasse, Florida
Juneau, Alaska - though you could use Cascades and the Alaska Marine Highway
Honolulu, Hawaii
State capitols with Thruway service only:
Boise, Idaho - was served by the Pioneer - has Thruway (arf-arf) Bus
Phoenix, Arizona - was served by the Sunset Ltd - has Thruway bus
Sante Fe, New Mexico - does have Thruway Bus
Baton Rouge, Louisanna - does have Thruway Bus
Madison, Wisconsin - does have Thruway Bus
Montgomery, Alabama - does have Thruway Bus
Columbus, Ohio - does have Thruway Bus
Augusta, Maine - does have Thruway Bus
Concord, New Hampshire - does have Thruway Bus
Dover, Deleware - does have Thruway Bus