  We prove that the mirror map is the SYZ map for every toric Calabi-Yau
surface. As a consequence one obtains an enumerative meaning of the mirror map.
This involves computing genus-zero open Gromov-Witten invariants, which is done
by relating them with closed Gromov-Witten invariants via compactification and
using an earlier computation by Bryan-Leung.
