There is a variety of Oaks in the areas you asked about, such as Pin oaks (Quercus palustris), overcup oaks (Quercus lyrata), scarlet oaks (Quercus coccinea), post oaks (Quercus stellate), willow oaks (Quercus phellos), bur oaks (Quercus macrocarpa), chinkpink oaks, etc.

There are red oaks, black oaks and white oaks in the forest in NYBG. Staten Island is really a mixed bag with swamp white oaks and chestnut oaks too.

The Oaks:

http://bhort.bh.cornell.edu/tree/theoaks.htm

Red oak

http://www.centralparknyc.org/tree-guide/northern-red-oak.html?referrer=https://www.google.com/

Tree walk:

http://www.centralparknyc.org/tree-guide/#tree-walk-tab

Hope this is helpful.