How can I use the sink function/ hydrology tool set to identify possible water catchment areas/ sinks in the landscape? So far, there's way too many of too many varying sizes. Is there a way to make it so only the sinks at the bases of hills are identified?
There are no tools to limit where sinks are found.
you can prescreen them as outlined in this document
Arc Hydro - Identifying and Managing Sinks.pdf - GeoNet, The Esri Community
There no tools to directly locate where hills are either.
What is the reason that you want to limit the process? If there is a specific area, you could just delineate it to form a mask and run on the subset and incorporate the result back into the original... as long as you don't try to use the resultant for further work