I've wanted to RP a Vigilant for awhile, but I'm waiting until the DLC in the *hopes* that there will be a full-on Vigilant questline. Fingers crossed.
Anyway, the difficult thing about being a Vigilant right now is that there aren't a lot of quests to support it. You can visit Vigilant locations, and help the random Vigilants you find on the roads and in the wilderness, of course. And I would help the Vigilant in Markarth, too.
Beyond that, I'd try to focus on the three threats mentioned by the Vigilants: Daedra, vampires, and werewolves. Sadly there are no werewolves you can hunt down in vanilla Skyrim, *but*
Spoiler you could always destroy the Dark Brotherhood. There's an NPC werewolf there (and a vampire, but she won't be there when you bust in). Justification for destroying the DB is simple: You look up Aventus Aretino with the intention of talking him out of contacting the DB. You then go to Riften, discover that Grelod is really a total witch, and kill her to save the children. Then kill Astrid and proceed to destroy their nest. Very righteous, I'd think - and very much in-line with the Vigilants' "at all costs" morality.
Vampires are a little harder to find unless you know where to look. I've only run across a handful of vampire lairs. But they are out there.
Last, there's Daedra. Unfortunately, in Skyrim you can't just stumble across some dremora or atronachs. However, several of the Daedric quests give you the opportunity to actually
betray the Daedric prince in question.
Some good Daedric quests for a Vigilant would be Vaermina, Azura, Hircine (though here you'd have to choose between the greater of two evils), Namira ... well I haven't done them all, but I'm sure there are others that would fit. Just approach the Daedric quests with the idea that your goal is to root out the Daedra or Daedra-worshippers, and anything you have to do along the way is part of the burden you must bear as a Vigilant. You can always back out of a quest and refuse to continue.
If that doesn't keep you busy enough, I would also include witches/necromancers as a target.
So I think there's enough for a Vigilant without trying to bring Bandits to justice too.