I have been to Gettysburg multiple times. Once did a guided tour of the battlefields with a guide. It was very interesting. I wasn't born in this country (WWII is the major battle I learned about) but it was still fascinating seeing sites and learning the history, since it is my new country I want to know as much as possible about it. It is a different understand to see the place and be told, here is where attacked, then retreated, so many people died here and so on.
What are some other interesting US Civil War battlefields or sites (Antietam, I would guess, Fort Sumter?)
Fort Sumter isn't really a major site (it's got a lot of name recognition, but not much happened there compared to other places).
Antietam is one - the bloodiest day in American history. Then there's a whole bunch in Virginia: The Wilderness, Spotsylvania, Fredericksburg, Manassas (site of two major battles). Further south, Vicksburg, Shiloh, Chickamauga, Stones River are all major sites. You probably haven't heard about any of these (maybe Manassas), but they're among the biggest battles of the war.
The Virginia sites are all huge, historically speaking. Shiloh is a particularly beautiful battlefield. Vicksburg is the most impressive, because it's one of the few with obvious remains of battle - it was basically a trial run for WWI. Most battlefields have a low line of earthworks and some craters, but it's tough to picture what they looked like.
The Battles of Manassas are known as the Battles of Bull Run outside of the South. They are both Southern victories and the first was the first major battle of the war.
Probably the most interesting thing about Fort Sumter is that so little happened there, in all honesty. That and seeing it on a map to understand why it was valuable.
Fredicksburg, Vicksburg, Sharpsburg (Antietam), Chancellorsville, Wilderness (Overland), Bull Run I & II (Manassas), Shiloh, Chickamauga, Appomattox... in no particular order ...but yeah you could spend your whole life just visiting the different sites and not see them all I reckon...
If you ever stop by a Georgia visitor's center, mention that you are interested in visiting civil war sites. I left with a 2 inch thick stack of pamphlets after the lady showed me everything.
What are some other interesting US Civil War battlefields or sites (Antietam, I would guess, Fort Sumter?)