The generally accepted best (AND most talked about) way to find a suitable side-project is to think about digital annoyances that you have in life, and how you would fix them. Scratching your own itch is called out as one of the best ways to find a side-project. It helps you to solve something that you experience yourself so it makes you kind of an expert since you have expectations that are not met. Those expectations might lead to a product/service.
PRO-tip:
Start by writing down things that you notice. I have a Trello board full of all my ideas. I organize them into columns Mind spins > Investigating > Serious > Executing > Done > Archive > Trashbin. I regularly go over the board and investigate the most interesting (most chance of being viable and least amount of work/fastest shipping possibility) and groom the board. Since I wrote down all my ideas I have enough to work on.

Talk to people; talk about stuff that's bothering them. Don't fall into the steep canyon of talking solutions. Go way back to the origin of the problem that they're experiencing, and think along from that. 5 Why's are also great here: ask them 5 times why to their answer to finding out the real issue.

Check out www.producthunt.com and search for "side project ideas" to find inspiration and tools to help you pick a side-project

Buffer has some great advice in this post on side-projects in which they talk about how they approach it and what projects they're currently up to. Check it out!

Google for side-project ideas