I think there's no database hosting on CodeSandbox, so you should use an external service.

Some services you can use:

• MLab (Free plan)
• ObjectRocket (Free trial)
• Compose (Free trial)
• MongoAtlas

MLab example

1. Set up a database at MLab
2. Copy and paste the connection string

A simple example function would be:

let initMongo = async () => {
  try {
    await mongoose.connect(
      "mongodb://<dbuser>:<dbpassword>@ds123456.mlab.com:49878/testdatabase",
      {
        useNewUrlParser: true,
        useUnifiedTopology: true
      }
    );
    return console.log("Database connected!");
  } catch (e) {
    return console.log("Database error!", e.message);
  }
};

Here's the documentation of CodeSandbox.