Building a web applications is definitely a good way to learn Elixir, as the ecosystem has very good tooling and learning resources centered around web projects.

That said, the web is not the only target for Elixir, as @kokolegorille mentioned already. Hardware devices with Nerves are a good one too in my opinion.

Some time ago, I wanted to help organize a beginner workshop to build an indoor air quality monitoring device with Elixir, Nerves and Phoenix. It runs on a Raspberry Pi, uses the inexpensive BME680 sensor, and presents a UI that can be browsed from a smartphone. It might not be ideal for complete beginners, but I still think it’s a great learning project for people with some experience with other programming languages.

I actually just implemented a similar hardware project this weekend, had some good fun, and ended up with something useful.