Off the top of my head I can think of 3 pubs I've drank in older than the U.S.
City I grew up in has a pub that supposedly opened in 1515, place is a dump and was definitely a box ticking exercise having a pint in there right enough.
There's a much nicer one in Edinburgh that although none of the original building's still there is meant to have been the site of a pub/inn since the 1300s and they claim Mary Queen of Scots ate/drank in it.
My favourite is just north of loch lomond and opened in 1705 as an inn for highlanders to stop at taking their cattle to market. Used to always stop there for a beer and some food after a day in the hills when I still lived in Glasgow.