Now, I am not one who is much into Contests or anything. I really only play in Contests when I am extremely bored. But it would be nice if they had a rival for Contests, too. But not in the sense where you just see them every single competition and he/she is hard to beat contest-wise. It would be worthwhile (for me) if they also battled you from time to time. And had a cute yet strong team, obviously with Chiraamii in it. XP
Then the actual "battle" rival could be from Hiun. I think it would be nice for once to have a rival like that: someone who you did not grow up with, but share an instant friendly rivalry upon meeting. You could encounter him maybe as he is fighting off a grunt from the bad team, and afterwards he talks with you, tells you a little about the bad team and what they're after at the time, and either battle you or give you his "#", so to speak (whatever kind of communication device they'll have or something along those lines). It could be very Lance-esque, with the whole intro of, "I'm a trainer, just like you" to make him seem normal and such. But then he has some strong pokemon. Perhaps, to fit in with the whole Yin/Yang idea, he could have been forced to work for the team, and throughout the story tries to break away from them but can't, then becoming a key factor in the triggering of >insert legendary-induced natural disaster here<, leaving you to solve it.
Maybe I got a little too into that one. But it'd be nice to at least have some kind of rival who doesn't spaz, act bratty, go from overly mean to extremely mushy, or somply battles you two or three times with barely-average pokemon. I just really liked how they set up Lance's character, and Hiun City is the perfect place to introduce such a mysterious, modest, and strong trainer.