UGA's "big" OOC rivalry is with Clemson. This presumes you ignore Tech of course. Clemson was almost always on the slate way back, but has been more sporadically of late. They are proximate, compete against each other for recruits often, and both are having a good run right now.
FSU would be possible but they of course are paired with Florida. Nobody else OOC is close until you get to NC, which is fairly close. Is proximity a need? Not always, ND-USC. Tradition > proximity.
Per Stassen, Georgia's most frequent opponents not currently in the SEC and UGA's record against them:
- GaTech, 109 games, 64-40-5
- Clemson, 59 games, 39-16-4
- Tulane, 25 games, 14-10-1 (NOTE, last game was in 1985)
- UNC, 24 games, 16-6-2
- Furman, 22 games, 20-2 (NOTE, last game was in 1950)
- Mercer, 21 games, 21-0 (NOTE, last game was in 1941)
- Virginia, 18 games, 9-6-3
- Miami, FL, 12 games, 7-4-1
- Yale, 11 games, 6-5 (NOTE, last game was in 1934
- Florida State, 11 games, 6-4-1
From my perspective, the GaTech rivalry is a good series. It is in-state so has proximity going for it. Also, I'm sure that a LOT of UGA grads live and work in the ATL metro area so this is an easy "away" game for them to get to, easier even than going to a home game in Athens.
Clemson would be a good one to get going again. It is just over an hour by car so an easy gameday drive (I drive more than that to get to tOSU home games).
Tulane, Furman, Mercer, and Yale are obviously relics of the distant past.
UNC would make some sense. It is five hours by car so not a terribly long trip and might help UGA to lure more NC recruits.
Virginia, Miami, and Florida State are farther away but would be good for occasional games.
The problem, I think, is that most P5 teams are pretty set on playing one somewhat equal OOC opponent per year and filling the rest of their OOC slots with creampuffs. GaTech isn't really a modern* "equal" for UGA, but that series does rotate H&H like an "equal" series.
UGA and GaTech as "equals"? Overall UGA leads the series 64-40-5. That is pretty equal. If you think about it, it means that in an average decade UGA has roughly won six and lost four. However, that isn't how it happened. Tech dominated the series early (5-1-1 in the first seven meetings) and went 7-5-2 before they became conference mates and 10-6-2 through 1928. Since then (1929-2019) Georgia is 58-30-3 in 91 meetings and it has been trending more lopsided recently with UGA leading 16-3 since 2001.
My personal theory is that even the high-end P5 teams are going to trend toward tougher schedules as it becomes increasingly difficult to sell tickets. It was already becoming more difficult for these teams to sell out their creampuff home games before COVID and my supposition is that the COVID interruption will only make that worse because some former ticket-buyers will not come back once they get used to not attending in person.
From your past posts, I gather that you would like to see UGA drop or reduce the games against Tech and replace them with what you consider to be better OOC games. I think instead that the increasing difficulty of selling tickets will cause UGA, in the long run, to keep Tech (because I assume that selling tickets to that game is considerably easier than a creampuff) AND add more high-end OOC games in addition to that.
Final thought:
I think that Miami might present a unique opportunity for UGA or another P5 school. Miami can't sell tickets at all because they have about four fans so it might make sense from the perspective of the Miami AD to be willing to agree to a 2:1 or 3:2 type A:H ratio. This could be a great deal for both teams. Georgia (or Ohio State or Notre Dame or any other large-fanbase school) would fill up the stadium for the Miami home games while Miami is a marquee opponent that would help the other school sell tickets to their home games. It would be a good deal for Miami because they would get a full stadium and it would be a great deal for UGA/tOSU/ND because they would get more home than away games and a marquee opponent to help sell home game tickets.