I'm really hoping that we get to see Kairi return to Radiant Garden in better conditions (maybe finding her grandmother), and sort of dealing with the fact that she was given a life she was never supposed to live.
I mean, she's happy being a part of the Destiny Islands and doesn't regret that, but I think there comes a time when she's going to have to realize that if Xehanort hadn't interfered, she would have had an entirely different destiny. And I could see her being interested in that.
KH1 also hinted that she knew Merlin as a child, so if she goes to Radiant Garden they can work with that, too (if they even remember it).
I want Kairi to want to try desperately to prove herself (in KHII she was always done with being left behind, so this is her time to shine), and perhaps even recklessly putting herself in danger this way (it's in her character).
I want her to worry that she's never going to measure up to Sora and Riku; and I want her to have abandonment issues--the idea that Sora and Riku will leave her again at the drop of the hat, and her trying to deal with that.
And going along with that, maybe she feels inadequate and sheltered, and that she can't empathize with those who have been so effected by the war, since she's been so little a part of it.
Her realizing her important destiny as both a Keyblade wielder and a Princess of Heart (who partly makes up all the light in the world, and if she--and the other princesses--falls, the light will expire) would be great; perhaps her even being protective of her fellow Princesses of Heart who can't protect themselves like she can.
Riku and Kairi interaction up the wazoo is something we need...
Perhaps Kairi having issues with fighting at first, because her passive PoH attitude won't allow it. But eventually she becomes okay with fighting against truly evil people who attack her first?
I want her to interact with Naminé, Xion, Aqua, and so many others. Roxas would also be a good idea, since they briefly met in KHII.
Seeing her interact with the Disney characters more would help a lot; she met Mickey as a child, after all (as well as Leon and them, who she actually knows from KH1).
Some stuff with her and Lea could be interesting. Though I, personally, don't want her to forgive him.
And more than anything, I want her to be involved and informed about things for once that concern her, and allowed to have agency and make her own decisions about her own life. So far everyone's been making her decisions for her, and know more about her than she does.
I also theorize that maybe if Kairi dies, or something, they won't be able to create the X-Blade (because Xehanort either needs her as a Princess of Heart or a Light for that to happen), so maybe Kairi could even think about sacrificing herself for the greater good. Maybe.
Honestly, there is SO much they could do with Kairi. And I really hope they go all out with it, now that we have the new technology that can help to develop her better than ever before (with her being able to say things on the field, if she's in your party and all that).
If they explained some of the psychic ability she's somewhat seemed to have before (sensing that there was something wrong with Riku, and that that once place in TWTNW was a graveyard, etc.), I also wouldn't complain.
And maybe even learning why she means so much to Sora? I don't really mean this in a romantic way, guys (and not even necessarily in a friendship one), but why is Kairi SO important to Sora, that he literally couldn't wake up without having every single memory of her restored to him? Why couldn't he have done without a memory or two, as DiZ said? And why is she his light, besides obvious ideas about that?
Edit 1: Oh, and her not wanting to Sora and Riku to be the only ones getting hurt, as she said in KHII.
Edit 2: Her facing Xehanort down for everything he did to her. And us learning if he, perhaps, sees her as an abomination, as she's an example of the "tyranny of light".
Edit 3: Kairi learning that Xehanort apparently used her to get Sora to the Islands the night it fell--and her feeling guilty about that, and being sick of being used as bait to get her friends into danger and for all they've had to sacrifice for her (like Sora stabbing himself and turning himself into a Heartless for her and stuff).
Edit 4: Her finally getting to see the worlds (like she also wanted) is for sure something we need to see, and it would be great if SRK could do this together--if at least for one world.
Edit 5: It would even be wonderful to learn what it was like for her to be like in Sora's heart, but I'm not getting my hopes up for that one, honestly.
Edit 6: Kairi dealing with her kidnapper, Saïx.