Not a martini drinker myself but every time we're in Vegas we come to The lobby bar in Bellagio. (Petrossian Bar) for a lemon drop. They use an old fashion recipe with lemon cello.
Not only are the martinis created old school, and spot on ... the ambiance is spectacular. A pianists pounds the keys while you sit in the ultimate venue for people watching.
It's a must-go!
Don't miss the flower gardens just outside the bar!