The scattering diameters of Sgr A* and several nearby OH masers (~ 1'' at 1 GHz) indicate that a region of enhanced scattering is along the line of sight to the Galactic center. The scattering diameter of an extragalactic source seen through this scattering region will be larger by the ratio of the Sun-GC distance to the GC-scattering region separation. This ratio could be a factor of a few, if the scattering region is far from the GC and only a random superposition with it, to more than 100, if the scattering region is within the GC. We have used the VLA to survey 10 (11) fields at 20 cm (6 cm) that are between 7' and 137' from Sgr A*. Our objective was to identify extragalactic sources and measure their scattering diameters so as to constrain the GC-scattering region separation. In order to find sources within these fields, we have employed pdf\clean, a source detection algorithm in which sources are identified in an image by comparing the intensity histogram of the image to that expected from a noise-only image. We found over 100 sources, with the faintest sources being approximately 3 mJy. The average number of sources per field is approximately 10, though fields close to Sgr A* tend to contain fewer sources. In a companion paper we combine our survey with previous observations of the GC, and we assess the likelihood that the scattering region is so close to the GC that the resulting scattering diameters cause extragalactic sources to be resolved out by our observations. A number of Galactic sources is included in our source catalog. We discuss the double-lobed source 1LC 359.872+0.178, potentially an X-ray quiet version of 1E 1740.7-2942, a shell-like structure with a central point source, and a possible radio transient.