Mysore is the place for big/good/vegetarian. I still think Viceroy is excellent for classic North Indian or Mughal food - at least as good as Tiffin, and far less expensive.
Keep in mind that if some of you vegetarians are vegan, anything on the skillet will have been cooked with clarified butter. You'll have to stick with steamed and deep fried items like iddli or vaddai.
Regarding Mysore, I can't emphasize strongly enough to ask for the tomato chutney. All batter items are served with coconut chutney and sambar, but the tomato chutney is out of this world.
Alex