I've been to Vesper bar many, many times. Each time has been wonderful. This is a great bar to check out if you like classic cocktails executed perfectly, in the coolest casino on the Strip. Their house creations are also excellent. They change seasonally too, so you know you are getting the freshest ingredients possible. It is a bit more expensive than other bars in the casino but they are so worth it.
When I come here I never really look over the menu with detail, because I know that literally anything I order will be excellent. There are only a handful of places in town where that is the case. I've had many cocktails here, and everything has been really, really wonderful.
From the outside it looks like there is no privacy since it's on the casino floor, but I would suggest you head to the back where there are booths, it is much nicer there.