From the alternate site, do I download the ArcHydroTools_x64 if I plan on loading it on a 64-bit, Windows 7 operating system. ArcGIS 10.2 is still a 32-bit application, right? Many thanks.
ONLY if you install the optional 64-bit background geoprocessing extension:
10.2.2 -- ArcGIS_BackgroundGP_for_Desktop_1022_140426.exe
10.3 -- ArcGIS_BackgroundGP_for_Desktop_103_141996.exe
If the 64-bit background geoprocessing extension is installed, then you must install the 64-bit .msi of ArcHydroTools. But again that extension is optional -- and most folks will have no issue with 32-bit geoprocessing.