Yes, in ArcGIS Pro itself, go the Project->Options->Application group->Share and Download tab and you see many options for Staging, Unpacking of packages, templates, files and offline maps. There is a radio button you can click "Ask where to save before unpacking" that you can set too. If you accept application defaults, they always go to your C:\Users\user_profile\Documents\ArcGIS Pro\Packages directory or others seen in this pane.