Best Intentions in Logan Square makes a nice one. I haven't had it, but I'd be willing to bet Pearl's Southern Comfort makes a solid rendition - it is the first NOLA place that comes to mind for me.
Otherwise, I think of it more about where serves really fine, classic cocktails - since that's really what it is...particularly bars known for their whiskey. Franklin Room, Tortoise Club, Maude's Liquor Bar, Bavette's all come to mind.
In the same vein as Best Intentions, another bar that has a very wide selection of "classic" cocktails and is a little more casual would be Money Gun in the West Loop.