Petrossian Bar should win the award for best people-watching bar in Vegas. Located just off the lobby of the Bellagio, it's the perfect spot to sit with a martini (or tea and crumpets if you want tea service) and watch people walk through the lobby or the gaming floor. And if you get tired of watching people--you're sitting near the awe-inspiring lobby's Chihuly glass ceiling sculpture.
The bar itself is decent--liquor selection is a little sparse (stocked with the liquor standards, but no pleasant surprises or smaller distilleries)-- and the price is over-the-top expensive (but c'mon, you expect that from the Bellagio). But you're paying for ritz and a piano player.
The food menu is not particularly interesting, but it's an excellent spot to sit and observe human nature.