[cryptolect]

My next step up from "Hello World" should be relatively simple for most languages.

Pick a public JSON API. Retrieve it over HTTP. Parse the JSON into a data structure. Print some interesting part of the data.

This exposes you to HTTP and JSON libraries in a new language, as well as working with data structures. For instance, in Go, the parsing JSON step forces you to write some structs and learn about marshalling.

[joshrotenberg]

I second this approach.

It lets you work with a few of the available libraries in the language (network, parsing, etc.), gives you some insight into data structures and helps you learn the idioms in API design in the language. It's also easy to do incrementally because you can typically get a single API working and then build from there. What's more, its fairly easy to write tests for, thereby exposing you to that languages testing libraries and methodologies. And sometimes you even come up with something useful that someone else might need.