Okay...some clarifications: the buildings of the Heeresverpflegungshauptamt are located were the US Army had the quarter masters and the PX(sp?)..the heart of Centerville, so to speak!
Additionally I'm not sure, if the Wehrmacht casino wasn't at the same locations as the US officers casino, maybe, maybe not. It is rather difficult to depict, as everyone here uses the american terms for those complexes and thus the former origin is a little bit blurry...
Generally speaking, the three main US barracks in Augsburg (Reese, Sheridan and FLAK) are all placed on former Wehrmacht Kasernen. As FLAK was a Anti-Aircraft barrack since 1936 and Sheridan "united" a former infantry barrack with a Kaserne for communications units of the Luftwaffe, I assume that some of the units located in the ancestors of Reese were the Artillerie-Regiment 27, Panzerabwehr-Abteilung 27(later Panzerjäger-Abteilung 27) and probably parts of Gebirgs-Jäger-Regiment 99 (especially 14.(Panzerjäger) Kompanie). The first two belonged to 27.Infanteriedivision which was set up in Augsburg and was later transformed into 17.Panzerdivision, whereas -now it gets a little sticky- the Gebirgs-Jäger-Regiment 99 was partially formed in Augsburg from parts of the former Reichswehr IR 19 which also seems to be the basical unit for the Wehrmacht IR 40 belonging to 27.ID. So, parts of IR 19 (Reichswehr) were located in Augsburg and used to build parts of both units. II.Btl. of GJR 99 and its Pz.Jg.Kompanie was later moved to Füssen.
IR 40 stayed in Augsburg till the war as far as I know, but was likely stationed in the Infanterie Kaserne.
That's it for the moment, sorry if it's a little bit confusing, but as I pointed out, there is a) few common information and b) hard to depict what is what.