A well trained staff.
I'm open to just about any kind of cocktail menu if the staff knows what they are doing. I'd absolutely agree with DaRiv18 that there are too many places where the cocktail menu is pricy and looks intriguing, yet a quick glance behind the bar shows that the bartender can't stir properly or keeps a super sloppy station.
Also, if you have a riff on a classic on the menu, the staff had better know how to make the original as well. I've been into places with a sour base/champagne cocktail on the menu named something "75" and yet when someone in my party asks for a French 75 they get nothing but blank stares.
On the other hand, if I see a bartender using proper technique and behaving like a professional then I'll absolutely order a cocktail off the menu and probably talk to the bartender about a bartender's choice for my second drink.