I would prefer baseball myself, but there's no reason we couldn't do two groups or multiple games if we had enough people. I also hope that those with more (or more recent) experience don't mind stooping down to the level of those of us who haven't played in any organized fashion since junior high

Some of the players in my league were probably cut by their junior high team.

I love playing, I don't care how good or not good someone is - and besides, this is supposed to be fun and anyone who takes it too seriously will be flogged and be forced to have the ASSCLOWN moniker for one full year.
I'm in the Richmond area but I know Fredericksburg and the surrounding counties pretty well and that would be a good halfway point for NoVa folks and Richmond-area people... such details could be hammered out in due time.
It's all up in the air right now. Whatever works best for the majority of those interested. For myself, weekends work best and time of year is mostly irrelevant.
My mom used to live in Fredericksburg and there are a couple of really nice high school fields down there who might let us use the field for a day if we pay rent (our fields average $50-/game up here, we could take up a collection).
As for time of year? At this point since it's short notice, I'd shoot for late in the Nats season or even into October. Baseball in the DC area in July and August is BRUTAL and I'm ten years older now.
On a side note, we should totally do this type of thing in Cooperstown on Doubleday Field someday.