Low Memorial Library and Fountain at Columbia University
Kerouac frequented the Low Memorial Library, quite unsurprisingly, a lot during his two stints at the Columbia University. The fountain can also be seen in a much publicised photograph of him and Lucien Carr.
Retracing Jack Kerouac 
On the contrary: it’s extraordinarily surprising. Low Memorial Library ceased to be the university library in 1934. By the time Kerouac rolled up, it housed administrative offices.