The Horse You Came In On Saloon, allegedly one of the oldest still-standing establishments in the United States. Its in Fells Point, a few doors down from Duda's. I haven't gone in yet, doesn't seem like a craft beer place but whatever, its relatively ancient Americana!
Update: From Mid-Atlantic Brewing News' Alexander D. Mitchell, in the comment below:
"We pretty much disproved the "one of the oldest bars in the United States" claim in a recent issue of Mid-Atlantic Brewing News. A past owner somewhat disingenuously extrapolated the age of the building/deed into the "age" of the business. During part of the time since the earlier-alleged start of business, it was owned by a local Methodist minister--and Methodists were notorious for being anti-alcohol activists in that era!"
So there you go - Ed.