..Back in R/S/E, Feebas was the first and pretty much only Pokemon of it's kind to evolve by enhancing a beauty stat of some sort. Not that I'm saying that those stats have to exist again (they were a pain to maintain, I know. x_x), but it'd be nice for Eevee to evolve via competing at contests, which is just a passing thought in my mind, I suppose. Something like that, like if it gets a certain ribbon, like Shivi said.
No, that'd definitely be cool. I mean, Eevee isn't really going from ugly to beautiful so maybe in that regard it wouldn't make perfect sense, but it at least to me definitely has a sense of beauty to it. They could also have it evolve holding the Prism Scale as well, as that caused Feebas to evolve in Gen V. I don't really see either these being it's evolution method, but it's possible I guess!