The list of Monuments in Uganda (National Cultural Sites) from from the Museums and Monuments Department of the Uganda National Museum is here: https://en.wikipedia.org/wiki/Cultural_Heritage_Monuments_in_Uganda
It's categorized by districts but lacks coordinates. Also does not use row templates, so it's not being harvested into the Monuments Database.
Existing Commons categories for the Monuments and their Wikidata items (if any) : https://petscan.wmflabs.org/?psid=25049002
Wikidata items of Monuments in Uganda: https://www.wikidata.org/wiki/User:Alicia_Fagerving_(WMSE)/Sandbox_Uganda