It's a very close tie between Jolteon, Glaceon, and Sylveon.
Jolteon is easily one of my favourites because it holds sentimental value to me, as it was my very first level 100. I've always loved Jolteon's design as well, the erratic electric-like design makes Jolteon rather appealing to me. Jolteon was also one of my all stars during Gen V Wi-Fi battles, so that's another reason why I love it.
Viability-wise, Glaceon might be one of the worst Eeveelutions, but I've always found it can fulfill an interesting niche on some of my teams. That, and Ice types are cool. Glaceon's design is also so nice. I'm really fond of the hair-like head it has.
Sylveon is just adorable. HAVE YOU READ IT'S POKEDEX ENTRY? IT'S ABSOLUTELY TEETH-ROTTING SWEET AND CUTE.