Go figure, The Local has a home-made veggie burger than can be modified to be vegan.
That said, I'd come here for a drink, regardless of the food. The Local is wonderfully atmospheric, cozy and elegant. I love the multiple bar areas, the enclosed nooks, and the homey feel of the joint; you feel like you could go in there on any given day and come out with a bunch of new friends. It also feels a bit like a time-warp in there; with the gorgeous woodwork and period details, you get a vague sense of what it might have been like to have lived in Minneapolis during the heyday of the early 1900s.
And, of course, they have a veggie burger ($10). I had it without cheese. Also, just in case, tell them to not use butter; my friend and I had a feeling that the buns were toasted with butter, but couldn't quite tell. Lastly, make sure to ask them for a potato bun, as their regular multigrain bun has eggs in it. Anyway, the burger was a large, tasty patty made with wild rice and chickpeas, among other things. I also liked that they provided cucumber slices, instead of ubiquitous pickles.
The burger itself was quite good. Not the best I've ever had, but it was definitely among the best I've had in the Twin Cities: hearty and flavorful. It held together nicely and had a perceptible kick to it.
My only gripe was that they slathered some sweet "tomato chutney" on the bottom bun which messed up the savory taste. That said, they were more than happy to get me a fresh, plain bun to fix that problem.
I also liked the french fries, which weren't oily and had a baked flavor. The curried potato crisps, however, weren't that great: they just tasted flat and the curry powder wasn't well-integrated on the crisps.
The service was friendly, prompt and unobtrusive.
Lastly, the beer selection here is slightly above average, but not terribly innovative. It skews heavily to the British-Irish-American side of things (not my favorite beer producing countries), but they have a couple of interesting drafts. Come here for the atmosphere, some fries and friends.