What kind of small project can I undertake now that I have free time?

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?

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!