I'll rank overall trips, not just stadiums.
1. LSU - Legendary place that has been a "large" stadium for quite some time. Huey Long had them build dorms in the stadium so it would get around some campus laws/rules at the time. They are now offices, I believe, but it is pretty cool to walk through one of the side doors and see the small halls and offices inside one of the largest stadiums in the country. Place has had all sorts of legendary games and instances occur such as the earthquake game, the live tiger mascot that lives across the way and used to be paraded around the field during games, the fourth down calls of Les Miles that all seemed to work out, and the overwhelming noise and energy from the crowd. Loudest stadium in the league.
Two things will happen if you attend a game here as a visitor - you'll get called Tiger Bait and you'll be offered some type of cajun/creole cuisine (jambalaya, etoufee, gumbo, etc.).
Definitely a must for a new league member. Pro move is to stay in NoLa Fri and Sat. Make a weekend out of it.
2. UGA - Homer pick I guess, but Athens is consistently ranked as one of the top college towns in the nation and the best in the southeast. Fly into Atlanta and get a shuttle/rental an hour, hour-and-a-half to Athens. Grab a hotel room downtown well in advance, and you'll be able to do most of the town just by walking. tons of restaurants, cafes, bars, shops, walking trails, etc, all in a few blocks of downtown. There is also a free art gallery and botanical gardens near campus that are quite nice. Sidewalks features stars where local music acts such as REM, B-52's, Widespread Panic, Daner Mouse, etc are immortalized.
Stadium was built in 1929 in a natural valley and visitors can look inside the stadium from a bridge that runs by one of the end zones. The famed hedges line the fields and our Uga mascots are memorialized with a mausoleum and statue in the corner of the west end zone.
Stands were built inside a valley that was created by a creek which still runs underneath the field, so it is built at a shallow grade. It doesn't lend itself to crowd noise, but the place gets plenty loud.
3. Tennessee - Venerable stadium that was built on the river. Place gets raucous and they have started a t shirt thing in recent years where they do a checkerboard by section. Looks pretty cool. The place comes down with the Vols run through the T.
Vol navy is overrated. Cool concept, but the draw to me is driving at Calhoun's or on "the Strip" pregame. Vol fans are absolutely insane online, but they are fairly cordial in person. Friendly group as long as you aren't a douche.
Can stay in Nash and drive in for the game or in some of the nearby mountain towns with mountain cabins. Right across the border in NC, you have a couple Harrah's casinos with sports books, but they are at least 2 hours away.
4. Arkansas - You guys have a rivalry with them, but it's a decent town and in a nice part of that state. Stadium has been renovated and is pretty nice now. Plenty of mountain areas in the Ozarks if you want that sort of getaway.
5. Kentucky - Stadium is pretty blah, but you can visit the race track nearby (Kenneland) and see some quality horse racing. Bourbon trail is also nearby if you'd like to learn more about America's whiskey. Lexington is in a beautiful part of the country with rolling hills and horse farms surrounding their basketball nirvana. this might be an even better place to go for a basketball trip. Cincinnati is 1.5-2 hours north if you want to catch a Bengals/Reds game and try some of the best chili in the world.
6. Ole Miss - Cool town and the Grove is a famous SEC tailgating experience. It is more of a drinking occasion than actually cooking food. You bring the food in with you and drink bourbon or beer under a tent that has a candelabra and on tables with silk tablecloths.
7. Mizzou - Unique experience for our league, but nice college town with plenty of places to eat and drink. Right in the middle of the state, so you can fly into and stay in STL or KC, each of which has plenty to do for a long weekend. Fans are very nice and lack the mean-spirited and assumption nature many SEC fans have.
8. Vandy- Terrible stadium, but "plenty of tickets available" and by far the best city in the SEC. You go for Nashville, not the stadium. or game experience. Vandy has a nice campus as well and is in a pretty part of town.
9. Auburn - Nice little town with plenty of stuff to do on gameday. You'll probably want to stay near Atlanta if you're going for the weekend and hang out there. Aub is about 2-2.5 hours away. Gameday traffic can be a mess, but if you go early enough, you'll be fine. Stadium is okay and the fans are in the game as long as they are competitive. You won't have the threat of violence here that you do on the other side of that state.
10. South Carolina - Located in a soup bowl in the middle of that state, it gets really hot and stuffy here. Not a bad town with a few places to go, but the pro move is to stay in Charleston or on one of the beaches 1.5-2 hours away. If the game is in Sept, dress for sun and heat. Also, thunderstorms pop up in the afternoon out of nowhere.
11. Alabama - Nice stadium that lords over the rest of campus. They have some nice campus buildings and a huge meadow in front of their chimes that is good for tailgating. Town is okay - another college town with a "strip" where there are a handful of bars. Mean-spirited fans that get upset over simply seeing the other team's fans. Some will be nice before the game, but the stories I've heard from there from all sorts of other fanbases are really bad. They don't take losses well, so if the Horns win there this year, be prepared to get out of there in a hurry. Here's a couple stories to read about their fan behavior - https://www.al.com/alabamafootball/2021/10/people-of-alabama-please-stop-shooting-each-other-over-football.html
https://www.nydailynews.com/sports/college/alabama-mom-attacks-oklahoma-students-article-1.1565867
https://krod.com/cop-delivers-epic-body-slam-to-alabama-fan-caught-throwing-drinks-at-opposing-team/
12. Miss St - Stadium is one of the oldest in the nation and there is little gameday traffic, especially for night games. Nothing nearby and a very small town, so that explains the ranking.
UF and A&M - never been to A&M for a game, but the stadium is very nice after the recent renovations and additions. UF I haven't been there enough to form an opinion, but it is within a couple hours of several beaches.