In Visual Studio 2012 all I had to do was enter:
(localdb)v11.0
Visual Studio 2015 and Visual Studio 2017 changed to:
(localdb)MSSQLLocalDB
as the server name when adding a Microsoft SQL Server Data
source in:
View/Server Explorer/(Right click) Data Connections/Add Connection
and then the database names were populated. I didn't need to do all the other steps in the accepted answer, although it would be nice if the server name was available automatically in the server name combo box.
You can also browse the LocalDB database names available on your machine using:
View/SQL Server Object Explorer.
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