This is even funnier to me because where I'm from, trains in cities aren't really a big thing, but trains BETWEEN cities very much are.

This map is outdated as the Lelle-Pärnu route isn't currently serviced, and missing some stops, but this is our railway map:

Tartu has 2 stations as far as I know, Tallinn has multiple, the other places the train stops are all small enough that only one station exists. Entire point of it is to get people into and out of the cities. In the cities we have buses and (only in Tallinn) trams, used to also have trolleys. But only the capital, Tallinn, is a place where you would take a train from one station to another within the city itself.

Most of these places are villages and small towns. The population of Puka is like 500. Orava is around 200.

Now we just need the Tartu-Viljandi-Pärnu route and maybe a Narva-Tartu route, as both would be used by a lot of students (Tartu is a university city), but unfortunately geography doesn't favour my idea, there's protected wetlands between Pärnu and Viljandi as well as between Tartu and Viljandi