The oldest building in Oregon isn't currently standing, it's a pile of wood sitting in a warehouse. Hopefully it will soon be reassembled in a new home. Pretty interesting, in that no one knows who built it or exactly when. The current theory is that it's of French/Metis construction. https://restoreoregon.org/molalla-log-house-a-progress-report-2015-2018/
Virginia's is apparently a church in Jamestown, which makes sense. I volunteered at the Jamestown Settlement for a summer in middle school (I was on the ships ... it was a lot of fun). It's kind of easy to take that stuff for granted, since I grew up in Williamsburg. My elementary school's playground shared a wall with the governor's palace. I was baptized in a church built in 1774, and my parents were married in a church whose current building was constructed around 1711.