"Southern Accents" is definitely the most nostalgic Petty record for me. I camped out in the parking lot of the local mall with my best friend to be in line for tickets the next morning (still can't believe my parents allowed that). Spent all the money we had getting tickets for us and our friends. On the night of the show, we were lucky that someone's parents were out of town, so that's where the pre-party was. Invited some beautiful girls (who were into it too), wore the concert shirts to school on Monday... It was everything good about coming-of-age... friendships, girls, freedom, rock music...
But with some perspective, it's definitely the most stylistically uneven Petty record. He set out to do a tribute to his home state and to the South, hired a couple guys from The Band, then hooks up with an English synth-pop dude in leather pants (who ends up co-writing a bunch of the songs). Hey, we should hire horns! In the words of the Surly: "What are you doing, Tom Petty?"
I agree that the title track and "Dogs on the Run" are underrated deep cuts. The drums and rhythm guitar intro to "Rebels" just instantly takes me back to all the excitement and possibilities of youth. "Best of Everything" is a great ballad. That's four pretty solid songs. I actually like "Don't Come Around Here" if only for the sneering spitefulness of the lyric. It has no business on a record that's a tribute to the South, but it's redeeming. Then there are a few songs that aren't at all southern... and they're really not even good songs ("Mary's New Car").
If I were a music critic, I'd put it middle-of-the-pack - easily behind "Torpedos," "Full Moon Fever," and "Wildflowers." As a mile marker of my life, it was (and is) bigger than all of them.