Yes, that of Vicksburg
Antietam Creek
Fort Sumter is a sea fort in Charleston, South Carolina. It was the site of the first battle in the American Civil War. It's now in Fort Sumter and Fort Moultrie National Historical Park.
The Battle of Tippecanoe happened near the present site of Battle Ground, Indiana. There are links below.
Gingras Trading Post State Historic Site was created in 1845.
The first pitched battle was First Bull Run (Manassas), which was in Virginia.
In South Carolina. It was the Battle of Fort Sumter.
The Confederates
Manassas Virginia. The Battle is generally known as First Bull Run.
civil war battle site
There was no real "first battle" of the Civil war because it started in different states after different battles. For example, the first official shot fired was at Fort Sumter when the confederates attacked unprepared and expecting union soldiers. The first big battle of the Civil War was the first battle of Bull Run/Manassas.
Battle of Carthage State Historic Site was created in 1990.
Battle of Athens State Historic Site was created in 1975.
Battle of Lexington State Historic Site was created in 1958.
Yes, that of Vicksburg
I am aware of no battle at Appomattox Courthouse, but it was the site of the surrender which ended the Civil War.
The Battle of Bull Run, July 21, 1861, which was the first major battle of the civil war, had spectators. See http://www.eyewitnesstohistory.com/bullrun.htm, " On the day of the battle, carriages filled with spectators eager to see the Confederate defeat flocked from Washington to the battle site"