tl;dr: Basically, I recommend Manassas or Baltimore, among many good choices. But you can read on.
A day trip from DC to Virginia? Those are some good ideas. And yes, for Richmond, you'd want Richmond Main Street Station, RVM, which has less frequency. The segment from RVR to RVM is quite slow, and from there the train goes on to Williamsburg. Both destinations are in super walkable areas. Richmond has transportation stuff like the Triple Crossing tracks, and the Canal Walk, on the only class 5 rapids in a major city, it is said. Other parts of Richmond are a taxi ride from RVR, like the VMFA museum, not that you need an art museum coming from DC, but it is top 10 by some measure, and is in a more tree lined part of the city, the part above the Fall Line. The Science Musum is in a former train station. Williamsburg I guess you know about, and the station is right there, three quiet blocks away. There seem to be fewer people in costume lately, but restaurants are holding steady. You don't need a ticket for the crunchy pedestrian street. They don't know whether to raise ticket prices or lower them to deal with the drop-off in people doing history as a family vacation. Still plenty of visitors. The old breed horses are popular. Shopping is too.
Manassas is even closer to DC than Ashland. Walkable, food, etc. There are two or three music events outdoors every weekend in the summer. Roanoke has the transportation museum. Also go to the Roanoke Weiner Stand and the rest of Market Square. The park with the star on Mill Mountain is a taxi ride.
Lynchburg has places downtown, on the river. Culpeper has a few, not on a river. Charlottesville is the twin of Williamsburg, for visiting. A lot more restaurants, but you've got some steps to get away from street traffic. Mel's Diner is real for very casual, up the stairs from the station. Go west to the university Lawn and Rotunda, or east to the pedestrian mall and historic Court Square. Monticello is a taxi ride. Ashland is exactly how you describe it, and I think Fred is too.
I find Baltimore wonderful if you want to go the other way, quick and easy schedule since you also have MARC. I'd go southwest from the station, solid neighborhood, beautiful. Example, Dodah's Kitchen on Charles Street, you won't even know it's vegan. Also there's Little Italy or the Harbor. Taxis are very cheap in Balto.