Mississippi.
Mississippi (state & river) Colorado (state & river)
Mississippi River is the name of the state and the largest river in the USA.
Yes, there is the River Styx in the state of Georgia.
Texas is the US state across the Rio Grande River from Mexico.
The Missouri River begins as Brower's Spring in the state of Montana.
The US state that sees the sun rise first is Maine. The best places to watch the sun rise are from Cadillac Mountain and Eastport.
The St Johns River is 310 miles long making it the longest river in the state of Florida.
Missouri
Mississippi is home to the Mississippi River
Mississippi
There is a capital in a non-US country on a "Red River", but I don't believe any US State capitals are ... Perhaps you are looking for Hanoi on the Hong (Red) river?