I've always found that one of the best ways to learn something new is to get my hands dirty and start writing code. But it also helps me to have a project to work on, and a goal in mind. You could always go the traditional route and build a to-do list. I need something that's going to hold my attention a bit longer though. With that in mind, here are a couple of ideas that have inspired me recently.
Hot JAMS(tack): Building a Music Discovery App with Drupal and React
Brian Perry gave a talk at DrupalCon Nashville about how he created an application for visualizing trends in popular music using Drupal and React. It's an interesting example, and I love how he's taken something he's passionate about and turned it into a learning opportunity. Find something to play with in this huge list of publicly available APIs.