You can put the DB file anywhere you like. For example, here's a connection string to connect to a database at C:\test.db
SQLiteConnection cnn = new SQLiteConnection("Data Source=c:\test.db");
When you say "I connect to it using sql explorer" -- I'm not sure what you're talking about.
Here's a video I made of me in Visual Studio creating a new connection, creating a table, inserting data into it and creating a typed dataset using Visual Studio and all the design-time support features of SQLite: