Flight
Spending your whole time in the Hudson Valley? Your best bet is probably ALBANY AIRPORT, which is about a 45-60 minute drive to Saugerties. If that doesn't work for you, the next option is NEWARK AIRPORT, which is a 1:45-2 hr drive to Saugerties.
Flight
Making a NYC Manhattan trip out of it? You might want to fly one of your legs in/out of JOHN F. KENNEDY AIRPORT or LAGUARDIA AIRPORT so you can have easy transportation to Manhattan and not need a car to get around for part of your trip. There is an AirTram to/from Manhattan and then you can easily transfer to the subway. You can also fly to one of these airports both ways if you can't rent a car. You can take the train down the Hudson.
Train
You can take Amtrak...
Hotel
Hotel
Hotel
If the blocks are already booked, here are some other local hotels: Holiday Inn Express & Suites Saugerties - Hudson Valley Address: 2777 NY-32, Saugerties, NY 12477 Phone: (845) 247-8800 https://www.ihg.com/holidayinnexpress/hotels/us/en/saugerties/albsa/hoteldetail Comfort Inn Saugerties Address: 2790 NY-32, Saugerties, NY 12477 Phone: 845-246-1565 https://www.choicehotels.com/new-york/saugerties/comfort-inn-hotels/ny016 Diamond Mills Hotel & Tavern Address: 25 S Partition St, Saugerties, NY 12477 Phone: 845-247-0700 https://www.diamondmillshotel.com/