A few of New York's favorite things:
State Flag: To the right. It depicts the figures of liberty and justice standing on either side of a shield. More information on the flag's symbolism and origin can be found here.
State motto: Excelsior, which is Latin for ever upwards.
State fruit: the apple
State fish: the Brook Trout
State muffin (yes, there is a state muffin): the apple muffin
State bird: the Eastern Bluebird
State flower: the rose
State song: I Love New York. You can read the words and listen to the lyrics here.
State insect: the nine-spotted ladybug.
You can find more information on New York's symbols at the Department of Environmental Conservation Website.
For quick reference facts about state geography or demographics, a good source is the U.S. Census Bureau.