Shwmae, Megan! The group in Fredericksburg doesn’t actually have events centered on the language, but our group in DC does – non-class conversation group, first Saturday of every month, Teaism Penn Quarter near the Archives-Navy Memorial Metro Station in central DC, 10:30- noon. You will be very very welcome anytime!
Our Washington DC Welsh Society – https://washingtondcwelsh.org/ – has other events, too: gatherings to watch rugby and football (aka soccer), a big St. David’s Day banquet coming up on February 23rd, a Christmas carol service, and other stuff. We’re a fun lot.
There are a few scattered Welsh speakers that I’m aware of around Virginia – one in Staunton, for instance – but the biggest concentration is definitely up here in DC. Where are you?