I am attempting to install SSDT v15.6.0 into an existing Visual Studio Team Explorer 2017 instance. When I run the SSDT installer, I can select Visual Studio Team Explorer 2017
This is currently broken due to a bug in Visual Studio - see this post on the Developer Community site: SSDT cannot install onto 15.7 version of Visual Studio
It'll be fixed in a forthcoming Visual Studio update, but if you can't wait for that a workaround is to completely uninstall Visual Studio and install an older version. See my answer here for instructions: https://stackoverflow.com/a/50349464/1184850