I am using VS2012 and I have a database created:
(localdb)\\v11.0 (SQL Server 11.0.2100 - T61\\Alan)
How can I find out the physical location o
Are you saying you can see it listed in SQL Server Management Studio? Right click on DataBase -> Properties -> Files will tell you where on your hard disk it lives. If you backup the mdf, be sure to back up the ldf too.

Alternatively, you can right click on the DB, and choose Tasks -> Backup. This will make a a single .bak file for you, and you don't need to worry about the mdf/ldf.