In Visual Studio 2015 Preview, I see the following vNext templates in the \"New Project\" window:
I was having the same problem, except that unlike the accepted answer suggests, the ASP.NET Web Application was not on the list of templates at all.
I was able to get it to show up after following the instructions from this article.
Tools -> Extensions and UpdatesOnline then click Visual Studio GalleryASP.NET Project Templates and download the first result.Alternately, you can download the templates directly here.
I believe this download actually is meant to install some other templates that I wasn't interested in, but installing them must have also installed the base template in the process. Either way, it worked for me.