Sorry for the slow response. Fell at work, ironically on my birthday, breaking my ankle. Lots of fun. But, speaking of the two ports, I have only traveled out of Bayonne.
I've heard good things about Baltimore, they have secure parking at the nominal $15 per day. They built a nice, new facility a few years back, so it is pretty comfortable on balance.
The cruise port at Bayonne is a converted Navy dock. Very large, wide-open. Pretty easy to access from the bus I rode into it from. The parking is secure, at least in that the entire dock facility is gated, and it is nearly a mile from the entrance to the parking area. They charge $19 per day. For my money, the experience of cruising out of Bayonne, with the New York skyline, Statue of Liberty, would be worth it. You can see many pictures of my short cruise on Liberty of the Seas in the Gallery.