My first four letters love to talk,
Most people like to Chat
the next three like some sun,
If you go out in the sun, you might get a tan
the next pair are quite interested,
Someone interested, might say "Oo!"
the last, a State, we’re done.
State could mean country, or US state. In either case, Ga is Georgia
I am a city in a state,
above the one before,
Tennessee is north of Georgia
our football team is really strong,
Blue fire from the core.
Thanks to @Rumpelstiltskin
This is the state football team - the Tennessee Titans, who have a logo with blue flames
Above me is a town of stone,
where crimson waters fall,
Thanks to @ChrisCudmore
This is Rock City and Ruby Falls.
Which are both at Lookout Mountain, which is the "Seeing Hill" referenced in the title.
My residents they often hear,
A locomotive's call.
This is the famous Chattanooga Choo-choo immortalised by Glenn Miller