Wild cockatoos enjoy eating & shredding the leaves, nuts, flowers & branches of the She-Oak. Brush Ironbark/Hickory Wattle Ironbark tree is from the Eucalyptus family and is safe for parrots. Brush Ironbark Wattle or Hickory Wattle is a type of Acacia, but it is also a type of Myrtle and toxic to parrots.
Union Square is within Flatiron District and Manhattan and bordered by Gramercy Park, Greenwich Village, West Village, East Village, and Chelsea. LaGuardia Airport: 20 minutes by cab with no traffic. JFK Airport: 30 minutes by cab with no traffic.
I'd stay in the Union Square area, or go a little south to like the Marriott on 4th and Market. You're near the Westfield Center (big mall downtown), near Union Square, and you can take the cute street trolley to Castro and Fisherman's Wharf.