Which "water hole" (bar) pre-dates the US independence"? You may still stop by I have a drink.

White Horse Tavern, Newport, Rhode Island, established in 1673 & Fraunces Tavern, New York City, established in 1762 are both candidates according to Esquire.com's "Answer Fella"

Also, some sites contend that John Lafitte's Blacksmith Shop, established in 1772 is a contender, though they are not real specific about when it actually went from being a smithy's place to a pub.

Another site suggest "The Horse You Came In On Bar" in Fells Point, Md founded in 1775.

Wow. A lot of places want the distinction of being around the longest LOL

Hum! The White Horse Tavern that I have was established in 1880, 567 Hudson Street, New York, NY.
The Jean Lafitte, in New Orleans, 1772 is what I was looking for. Here's my Source.

The 10 Oldest Bars in the United States

As I recall, you could always count on a drink at Lafitte's Blacksmith Shop, although I don't remember exactly when it officially changed into a bar. It was a long time ago, and my memory is hazy about my New Orleans days.