Right off the square* (or is that on? the square?) Local Tavern is a relatively recent arrival on the downtown bar scene. If you're looking for a relaxed place to get a beer with some friends then you'll like it. Not too college-y, and not too local-y (you know, the kind of place where regulars scowl at your from behind a pint and a shot of jager while they root for the Brewers), it's just right. Crowd on a typical weekend night is mid-20's early 30's young professionals and academics.
I suppose the beer selection is good, but I'm a consistent cheap beer drinker, so I can tell you've they've got Schlitz, PBR, and Old Style.
I've never tried the food, but I can't imagine it's either that good or that bad. Local Tavern is really a bar with a seating area. Sure, it's larger than your usual seating area, but, mainly, it's a bar.
Not bad.
*For you non-Madisonians, the Square is the center of the Isthmus where the Capitol is located, which is the tallest building downtown - I think. You've seen it in all the pictures. It's really quite pretty late at night in winter. Big, illuminated, looming over this sleepy upper midwestern college town and state capital.