Yuck. I hate HPN and used it only once for this reason.

I think there is a hotel with a shuttle, but it's on the other side of HPN from the airport, and I didn't stay there because it would be a long taxi ride from the White Plains train station.

I stayed at a hotel east of downtown (sorry, forgot the name). I took a taxi from the train station to the hotel, and arranged for a taxi in the morning to HPN.

I should have walked from the train station to the hotel, because the taxi fare was $16, and the taxi dropped off three other people first. It didn't save any time and cost far too much money.

The ride from the hotel to the airport was a nice vehicle, non-stop, and costs about the same.

If there is any way to fly to EWR or LGA or JFK instead, do it!