I've been having this problem for about a month, and I am completely stuck.
Under the "New Project" window I don't see the windows 10 universal templates, but have the sdk and tools installed.
All pictures are in this folder on dropbox.
New Project Window: Capture.png (on dropbox)
What I tried:
Okay, so for anyone having this problem:
Check if the "Windows Installer" service is running under Task Manager/Services.
If not right click and select Start service.
After that run the installer for Visual Studio and select repair.
After the repairing finishes, (reboot if you want, it wasn't required for me) all the templates are installed.
(And yes, if you still have this problem, write to microsoft, they are helpful in these kinds of questions)