I think that visiting day is very worth it, and the harder it is to come, the more worth it it is. It is a great opportunity to show your kid how interested you are in what he is doing, that you drive a whole day in traffic just to do so.
Just shut up, get your kids a DVD player (uncle moishe of course), get yourself a book on tape, pack a cooler full of soda and a box full of potato chips, and drive.
Personally, I would forget the whole motel thing, and bring a big tent instead, and then spend the night at a park upstate with a big barbeque and a fire and ghost stories.