Build something you're interested in something you would use.
You could also pick out a new language or skill set you'd like to learn and use that so it's a double win.
There will be others like you that find it useful.
Kaggle!!! National Data Science Bowl, if you like AI / machine learning, it's the way to go. You'll know interesting people and collaborate with them, and there are chances you can win money and put results on your resume!
First thing, change post to an Ask HN.
Second thing, add more detail ;)
Add more detail about your interests, previous projects and skill sets.
How much free time? 10,20,30 etc hours per week?
How long will this free time last? A month, a quarter, a year?