VS2012 setup spoils SQL Server 2012 Data Tools for everybody or just me?
I had a similar problem with my installation of VS 2012 (Premium). I installed VS 2012, at the custom installation options screen I chose the option for SSDT, but when actually using it, it was really absent (same error as yours).

My idea is that the default installer only adds the template for the project, but not SSDT itself. I also had to install SSDT separately (in this case only for VS 2012) and it worked (SSDT for VS 2010 is necessary only if you want to open SQL projects in VS 2010, but I guess you know that already).