Is the Downtown location worth it if you are seeing Broadway? I love the dining there and the casual dining rather than the more formal of midtown UES. But NYC Traffic is really bad what to do? Park Hyatt to even Central Park was really awful. And my dad has trouble walking so sans trains!
The trip from that location to the Theater District is quick and easy ONLY if you can take the subway. Because your father has mobility problems, as you have said, I would not recommend staying in that neighborhood.
That really is not the area to stay in with mobility problems. Its a super trendy area as well. You are better off in the 50s which is a short cab ride.