A recent comment suggested implementing the Snake game [0]. Conway's game of life seems to be another common one. I think some people have even mentioned implementing hackernews clones.
[0] https://news.ycombinator.com/item?id=21414791
I mostly go with a file uploader - sort of like Imgur but for anything. Solves the following "issues":
* MVC architecture * Relationships (files belong to user) * Authorization (user can only see files they uploaded) * Talking to third parties (store files in AWS?) * General UI/UX like displaying the files in a nice way, providing direct links or embedding, etc
Lastly, you can turn this into a API-only backend and then go crazy with any frontend framework you want!
I say early facebook cause I feel that doing a login, and feed page, and allowing status updates, friends search and confirmation, and a profile page with photo uploads to be a pretty good intro stack.
That said for a new language I ALWAYS look for a modern koans exercise to do. Some langs have them, some don't.
This provides me enough math, control logic, looping and display logic to see what's what.