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 can add tables with EF but if I right click on Tables in Server Explorer the only options I have are Refresh and Properties, i.e. no Add Table menu option. Similarly, if I right click on one of the tables EF has created I also get only the Refresh and Properties menu options so I can't add rows, etc. Same problem with stored procedures; I can't add any (should I want to do some testing with EF and stored procedures) because I only have the Refresh and Properties menu options.
FOLLOW UP: I have isolated this problem to VS2012 Professional. When I use VS2010 it works exactly as expected: I can add tables and stored procedures. Following the same steps with VS2012 results in the situation where there is no menu option to add either tables or stored procedures. I produced these test results with SQLServer 2012 LocalDB.
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 .
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.