Like the last post said, they keep you there about 10 days. The main reason they do that is to make sure you do not have a CSF (brain fluid) leak before you leave. If you have CSF leak, it usually requires a second (not as long) surgery. These almost always happen within the first few days, so staying there 10 days is long enough. They make sure you are good before you leave town. I flew from NY and very glad I did. I am on the cautious side, so I stayed an extra week just to be sure. Was not really necessary, but that's just me.
In rare cases a person may develop Meningitis after coming home. I heard of one case like that (not from House) and the person was treated by a surgeon locally.