The vehicle in the photo with my grandfather has been identified by a national car club as a 1910/11 Renault but the model seems to be a Landaulet rather than a towncar.
I have conducted a fruitless search to verify whether or not Col. Astor owned such a vehicle --- car clubs & museums, Renault history, old newspapers, photo archives, etc. If any car buff (or Astor fan) has any books with photos that may show such a vehicle, I'd appreciate hearing from you.