Save for Agrabah and Hollow Bastion, the first time you go through some of the revisted worlds from KH1, you finish up the story from the first movie. I haven't gone through some of the worlds a second time to confirm this, though in Port Royal and Pride Lands, I know that cleared the plot from the first movies.
In Agrabah, you go through Return of Jafar. Hollow Bastion is Traverse Town this time around.
You have to kick 1000 Heartless asses. IN ONE FIGHT. Luckly, there's only two types of them, and both have easy-to-use, multi-enemy-asskicking reaction commands. And you will level up two to three times on that fight alone.
The Cloud/Leon dialogue, which is a bit before you get to that fight, sorta rules.
Cloud and Sephiroth do meat face-to-face in the game... And then you hear what I think was Aerith. Of course, my first automatic thought was '... Oh fuck, not again. >:/'
You finally see Mickey for more than 30 seconds, and you get to see him get pissed. Like bad-ass pose, get down to kicking ass pissed. Too bad you can control him/get him in your party yet.
Lion cub Sora. And chibi. Fairy. FF X-2 girls. Augh, the overwhelming cuteness in this game! It will rot you insides because of it!
And AC, non-breasticular Tifa FTW.
Okay, Valor Drive is easy to level up, because you're right there near the Drive EXP orbs. (Those yellow ones, which replaced those regular green EXP orbs from KH1, IIRC.) Wisdom Drive is kinda hard to do since you're shooting them from a distance. I haven't really messed with Master Drive yet. (Though I know I kicked some enemy's asses with it.) I don't know how I did it, but I did use the Dark/Anti Drive, which... really doesn't suck. No Keyblade, reactions and such, but you turn into a quick little combo monster. And I want to get into a cut-scene with it activated, just to see what happens. :P
Mini-Gummi ships. I'll leave it at that.
Work first, then back to the game.