Eek... overnight parking could be expensive. If you park in the NYU garage, can the admissions office validate your parking stub so that there will be no charge? That's what they did at Tufts. It might be a good idea to call and find out.
Otherwise, you could try driving around for a while the night before to find a spot in the street... where you wouldn't have to move it in the morning. Even if you have to park further away, taking a cab would still be MUCH cheaper than spending $30 on the garage. 😎