The substitution of Zn for Cu in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (YBCO) causes a surprisingly large suppression of the superconducting transition temperature. However, there has been some controversy as to whether Zn replaces Cu in the ${\mathrm{CuO}}_{2}$ plane sites, Cu(2), in the CuO chain sites, Cu(1), or in both sites. We present x-ray-absorption fine-structure (XAFS) data for samples from four different sources with several concentrations of Zn. Our data indicate that, in many samples, much of the Zn resides in ZnO (or ZnO-like) clusters; for some of these samples we have estimated the amount of ZnO present from our XAFS data. One group of samples showed no evidence for ZnO-like precipitates, indicating that in this case, most of the Zn is in solution, or in a YBCO-like environment. For this data Zn has about five nearest O neighbors at approximately equal distances of 2.03 \AA{}. Furthermore, the distances to the Zn further neighbors are well defined, with little broadening. Our analysis indicates that Zn primarily occupies the Cu(2) plane sites, in contrast to Co and Fe, which reside in the chain sites. However, its local environment is significantly distorted; the Zn(2) atoms are displaced along the c axis toward the Cu(1) sites by about 0.2 \AA{}. It is not clear whether the Zn atoms are uniformly distributed, or whether the observed distortion signifies some type of clustering; however, the sharpness of the transition supports a uniform distribution. Our work illustrates further the general tendency of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ to distort easily when slightly modified.