Thanks to this answer: How can I output NLog stuff to the vs2008 'output' window? I can now output from NLog to the output window in Visual Studio.
My follow up question now is: How do I set which 'Show output from' window it appears in, so that I can keep my logs for different things separate? (And also avoid all the ASP.NET noise in the middle of my logs).
There seems to be a 'JavaScript Language Service' already in there, along with the usual 'Debug', 'Build' and 'Build Order' output sources, so it seems like it's possible to use different sources - but I couldn't find any information in the System.Diagnostics help pages.
I'm using Visual Studio 2013 and NLog 3.0 by the way.