Entity Framework Code First can't find database in server explorer

Looking at your config (supplied during chat) I can see that your EF is using localdb and MSSQLLocalDB instance. Try:

(localdb)\MSSQLLocalDB

I figured out where my database is by doing the following:

• put a breakpoint in the first place where I call context or dbcontext or whatever you want to call it
• when you're on that breakpoint, drill down into Database -> Connection and somewhere in there you'll find your connection string.