Dr. Schwartz is a fantastic neurosurgeon, so your husband is in very good hands.
I would definitely recommend Seton Hall. It was very quiet when we were there. One floor is used for guests and only a few other patients/families were there during our stay. It was by no means an environment with many patients and sick people around to depress you. For us, the convenience of Seton Hall was of most value. Los Angeles traffic can get pretty bad and the neighborhood is not the best (it is safe, just many homeless people), so staying there would allow your family to walk back and forth as needed. There is even an underground walkway that connects the two buildings for added security or the unlikely event of rain. Just keep in mind that Seton Hall is very basic, but clean and has everything you need. The rooms have a queen bed, pull out sofa, flat panel tv, and wifi. Some people on this forum stayed elsewhere after surgery to be in a nicer vacation-like environment, but I wanted the convenience of being next to the hospital just in case something happened. It never did, but am still glad we stayed there. We were able to walk to the hospital cafeteria for some meals. Seton Hall had a kitchen with a microwave that you could heat up food purchased at a nearby grocery store. There weren't too many nearby walkable restaurants, but we had a rental car for the days we wanted to eat or go elsewhere. Seton Hall also had washers/dryers and an unlimited supply of washcloths and towels (self serve), which was great for me after surgery. If you decide to stay at Seton Hall, I'd recommend you email them. They respond much faster than if you called and left a voice mail.
Your husband is lucky to have you taking care of all of the research and details. If you have any other questions, feel free to reply or private message me. I wish both of you success and a fast recovery.