I bring all of my friends who come to visit to The Weary Traveler. No one has been disappointed.
I moved to Madison from Minneapolis a few months ago, and this place is definitely a favorite of the places I've tried. The West of the Andes sandwich with roasted veggies is one of the best sandwiches I've ever had.
The servers are super accommodating. It was crazy busy last time I was there, and our server came back to mention to my dairy free friend that there is butter on the bun of the burger. My friend was impressed and said most servers wouldn't take the time to do that.
Only warning is not to bring anyone hard of hearing; it's really loud at dinner time. But otherwise the ambience is pretty perfect. Pretty diverse crowd, too, which surprised me a little.