My geography has apparently failed me, as I see nothing left.
Rhineland Palatinate, and Saarland, are completely west of Frankfurt am Main.
Baden-Württemberg is entirely south of Frankfurt am Main.
Thuringia and Sachsen-Anhalt were DDR.
Hesse and Bavaria, as well as Berlin, have been ruled out.
The only partial states remaining east of Frankfurt am Main, and south of Frankfurt an der Oder, are the extreme east of North Rhine-Westphalia, and the extreme south of Lower-Saxony, neither of which would I describe as being "geographically you are far off" from Hildesheim.
What have I overlooked, or what answer have I misconstrued?