Unfortunately, American "pubs" are little different from our clubs or sports bars with unbearably loud music or twenty televisions playing every flavor of ESPN. Nearly every alcohol-serving establishment I've been to in my region (Washington DC) is pricey, deafening, and not conducive to any sort of socialization beyond drunkenly grinding against strangers. I hate it.
There are plenty of small, quiet beer and wine bars here in LA that seem similar to the UK “pub experience”. Are you sure there aren’t many like that in DC? I would be surprised.
Tip: Look for places that serve espresso and/or tea.