Usually connect to an external database but I wanted to fiddle with creating a project with a local database. I am using SQLServer Express Local Database, not CE.
I
I had a similar problem only with Visual Studio 2012 Express for Web following along with the "Getting started with ASP.Net MVC3" at www.asp.net. The tutorial used a Sql Server Compact edition but I have SQL Express 2012 so I changed the connection string to have the data source point at my local instance, .\SQLExpress2012. The app worked fine and was able to read and write to the database. However I could not edit the database in the Visual Studio Express Database Explorer (all the context menu options were missing except "refresh" and "properties).
I found that changing the data source in the connection string to "Data Source=(LocalDB)\v11.0;" fixed the problem. I read somewhere that if you use LocalDb instead of the SQL Server instance name then it will be accessed under your user account - must have been some kind of permissions issue.
The whole (working) connnection string is: "Data Source=(LocalDB)\v11.0;AttachDBFilename=|DataDirectory|Movies.mdf;Integrated Security=True;"
Hope this saves someone a bunch of hours pulling their hair out, I'm almost bald now :)
I found that when installing Visual Studio 2013, I had not requested the 'SQL Server Data Tools' feature.
By re-running the installer from 'Control Panel' > 'Programs and Features', using the 'Modify' option, I could add the missing feature. On completion, the 'Add New Table' menu item was available.
If you only see Refresh and Properties when you right click on Tables in Server Explorer, you probably need to install SQL Server Data Tools from http://msdn.microsoft.com/en-us/data/hh297027 .