Quiet spots across from Don Davis Park depending up the specific street you park on, most with the default 16 hour parking in Newport and some posted for 12 hours. Other spots in the Nye Beach area are available with the same restrictions.
Bathrooms at Don Davis Park and near the beach.
I stayed in the preforming arts parking lot. No issues. Great space. Walk across the street to the beach, lots of shops, restaurants, not too loud. Was there on a Sunday night in November though.