Anything where I have a well-defined thing that I want, but I don't have the talent or expertise to do it myself. For me that's design work, but for you it could be setting up a database, creating a kernel module, etc. I view outsourcing as a way to save money in the long term, but good outsourcing should cost a lot up front. If you're looking to save money <i>right now</i> by outsourcing, you are probably going to get what you pay for.
I've been considering outsourcing the creation specific ReactJS (and react native) components where the interfaces/state can be defined by me.
Integration if you don't know the system you have to integrate with. Establish some sort of a protocol (simple example: passing xml data), ask what this other system needs as input. The rest of integration I'd outsource.