I’ve downloaded the final version of Visual Studio Community 2015 and the LocalDB was not automatically installed.
Yo can download it from Download Link
Choose installer as per choice and machine compatibility: LocalDB 64BIT\SqlLocalDB.msi or LocalDB 32BIT\SqlLocalDB.msi
Also note that
In Visual Studio 2012 localdb connection string is:
(localdb)\v11.0
in VS 2015 localdb connection string changed to:
(localdb)\MSSQLLocalDB
Muhammad Hassan 