Olivor Twist (Olive or Twist!? - I love puns!) is a great little martini bar in Willoughby. It's definitely a more sophisticated crowd, great for new dates or a girls martini night. It is kind of a quiet atmosphere, but when I was there the Indian game was on the televisions.
The martinis are actually really good and there was quite a long list available. I probably would never find myself at Olivor Twist on a Friday or Saturday night because Willoughby has much more exciting venues, but a nice night-cap on a weekday will work!