I have the same issue, I have VS2012 and ArcGIS 10.2 trial installed. I installed ArcGIS Runtime SDK for .NET version 10.2.4 and I still don't see the arcGIS templates under C#. Even if I select Framework 3.5 I don't get them.
Could you help? Thanks
For ArcGIS Runtime SDK for .NET 10.2.4:
https://developers.arcgis.com/net/desktop/guide/system-requirements.htm
Thanks,
Mohini