We just released a new version yesterday that lets you pick and quickly deploy. The notebook server is always local to your dev machine but you can run your Python kernels (one for each notebook session) locally with user credentials or in a GCE VM with a service account to access GCP services like BigQuery, GCS etc. The latter provides code closer to data in cloud but incurs charges while you keep the VM running.
More background: VMs (AppEngine Flex or GCE) are shared resources in a project that are typically accessible to all authorized project members. Hence storing user token on a such a shared resource presents some security concerns. Whereas your dev machine (laptop, desktop, ...) is typically under your exclusive control. Hence the two design points.
Thanks.
Dinesh Kulkarni
Product Manager, Datalab & Machine Learning, GCP