google a list of 'classic cocktails' and try and find something that strikes your fancy. it really depends on the type of bar you visit, but more upscale places should be able to make any of the 'classics' despite them often not being on the menu.
But besides that, you should try a Moscow Mule if you haven't. It's a simple, tasty drink you can get at basically any bar.
oh, one last thing, if the bar is empty, chat with the bartender and ask what they think!
