I found that when converting a project, I had to manually change the csproj file for the web application. It needs one additional projecttypeguid to show the mvc stuff when you do add new item.
Below is the corrected version:
<ProjectTypeGuids>{603c0e0b-db56-11dc-be95-000d561079b0};{349c5851-65df-11da-9384-00065b846f21};{fae04ec0-301f-11d3-bf4b-00c04f79efbc}</ProjectTypeGuids>