New York States Havens:

Addison
Albion
Alexander
Alfred
Alma
Amenia
Amity
Andes
Arcade
Argyle
Attica
Avon
Babylon
Barker
Bath
Bergen
Big Flats
Boston (ironically...)
Brant
Burns
Byron
Cairo
Cambria
Cameron
Campbell
Candor
Canton
Cape
Catskill
Centerville
Cherry Creek
Chili
Clermont
Conklin
Comwall
Cuyler
Danby
Darien
Dix
Eastchester
Edinburg
Ellicott
Evans
Farmersville
Floyd
Gaines
Gainesville
Gates
Glenville
Grafton
Great Valley
Greenport
Both Greenvilles
Guilford
Halcott
Hamlin
Harpersfield
Hartland
Hartwick
Hector
Herkimer
Homer
Hope
Hype Park
Independence
Jasper
Jefferson
Junius
Keene
Kendall
Knox
LaFayette
La Grange
Little Falls
Lorraine
Lysander
Marilla
Moira
Montour
Murray
Nelson
New Baltimore
New Scotland
Norfolk
North Castle
Nunda
Olive
Orwell
Oyster
Palatine
Parma
Pike
Pine Plains
Pittsford
Portage
Prividence
Putnam
Redfield
Richland
Riga
Rose
Russia
Rye
All the towns with St. in their name
Salina
Scarsdale
Scriba
Seneca
Smithville
Southeast
Sweden
Theresa
Thompson
Thurman
Triangle
Tuxedo (funnily enough...)
Tyrone
Both Unions
Urbana
Varick
Vestal
Veteran
Vienna
Volney
Waddington
Waterloo
Watertown
Waverly
Webb
Wells
Western
White Creek
Wilna
Windsor
Wirt
Woodbury
Worth
Wright
Yates
York
Yorktown