You didn’t mention what your child might want to do with a law or grad degree, but if it’s work in politics or DC, then W&M might have a bit of an edge for placement. There’s a decent amount of DC outreach and internships, and there are usually some interesting adjunct professors or guest speakers from DC.
At the end of four years I was ready to be done with Williamsburg, but living adjacent to CW has some interesting benefits. I used to study in the colonial gardens, and go running through CW almost every day. Yes, the town rolls up the sidewalks when the tourists go to bed, but that just means that the students depend on each other and on campus activities for their entertainment. If students want to go see a “big” concert or similar, Richmond is 45 minutes one way, and Norfolk/VA Beach 45 minutes the other way. A bigger issue for you might be airplane access. If you aren’t a driveable distance away, then it is kind of a pain to get to a decent size airport. If you are on the 95 corridor though there’s an amtrak station not far off campus (I used to walk to it) and it’s pretty easy and reasonably priced to get a train to DC and points northward.