If you don't get any geographic/datum transformations, that usually means we couldn't recognize either the input or output geographic coordinate reference system. The geographic/datum transformations contain the input/output geographic coordinate reference systems.
While a person can tell it's WGS 1984 being used by Web Mercator or that the state plane zone is using NAD 1983, the software is stricter. When you look at the layer properties in ArcMap, does either one say the coordinate reference system's well-known ID (WKID) is zero? If so, try redefining the coordinate reference system of that dataset. There's something in the definition that doesn't match what ArcGIS expects.