Despite serving animal products - although no dairy - I visited Eucalyptus because of it's high rating in TripAdvisor (It was not yet listed in Happy Cow). Most of the menu is vegetarian and they happily accommodate vegans. This is a kosher restaurant so you don't need to be concerned about dairy. Lots of fresh and local ingredients. Creative menu. Reservations are recommended. Closed Fridays. Saturdays are open for dinner only after 7pm.
Consider that most veg/vegan restaurants in Israel are kosher and therefore closed on Fridays and Saturdays (some serve later dinner). Eucalyptus is open both Fri and Sat.
Cons: Serves meat