Hi Matthew,
Please see this knowledge base article, and also this one. This should help you understand how to get a users default workspace, and also how to set the workspace for your API request. You cannot run a query against the public API to see what a user currently has selected as the workspace in the UI, as that is stored internally. You can get or set context from an AppSDK application, but those run internally within CA Agile Central. Here is a KB that talks about context within an AppSDK app.
Thanks,
Sean Davis