Agreed with peggyd - lots of great areas.
I highly recommend Rock Creek, Great Falls, C&O canal trail, Potapsco MD, Cabin John (running).
Within an hour you can hit so many different and awesome areas. Also, most of the orienteering maps (QOC) also are great places to trail run as well as orienteering.
If your other half isn't planning to have their own vehicle, for orienteering events, he could probably catch a ride with someone in the area. I also recommend looking into different options to rent/use a vehicle to get a little further away as many trails aren't easily accessible using public transportation.
Additional Links to consider for longer trail runs/hikes:https://www.hikingupward.com/maps/full_map.asphttps://www.hikingproject.com/
I also recommend EX2 for trail races. I have enjoyed the few I have participated in.
I personally haven't found any places to specifically avoid with the exception of a few areas in DC proper (but I wouldn't want to run/bike there because of all the roads, traffic, and stop lights.