Metuchen Inn is certainly sophisticated enough for the food snobs (and the setting is in an impressive almost 200 year old mansion) and they have some vegetarian apps and will modify the pastas to hold the meat/seafood upon request (but very few vegan options). Irving Social in Rahway has a very good and eclectic menu (plenty of vegetarian options - not as snobby as Metuchen Inn) and is in a very cool space, including one of the best al fresco spaces in CNJ, IMO (it's an interior courtyard that is gorgeous). The Garlic Rose (Italian-ish) in Cranford is also quite good with plenty of options, some of which are superb. Have had work dinners at all of these places and had almost all happy customers.
Following up on
@Knight Shift's post, Chez Catherine is one of the best French restaurants in NJ, so you'll impress folks, but they don't have a single vegetarian option there for dinner. Sweet Waters steakhouse is very good, but also doesn't have much for vegetarians.