We will study the geometry of cluster varieties from the perspective of stability conditions on the associated Calabi-Yau-3 triangulated category. I will focus on ideas introduced by Gaiotto-Moore-Neitzke which suggest how to produce cluster coordinates from stability conditions. In particular we will consider the class of examples associated to triangulations of marked bordered surfaces for which the cluster variety is a moduli space of rank 2 local systems and the space of stability conditions is a space of quadratic differentials with prescribed singularities on an associated closed surface.