My bet would be on research and entertainment. I feel like while these will be partially automated earlier, it will be a while until we manage to fully automate them.
Research is probably going to be automated before entertainment, but especially the human behaviour research, where again you need to have a good understanding of human emotions etc I would imagine will take a while. Also, we still can't fully understand how ideas come into our minds, it might be more than just random connections and memories.
Entertainment is highly connected to humans, empathy, emotions etc, which I expect it will take us a while to fully understand and thus 'teach' computers about, or help them learn about it themselves. Actually, I think entertainment is going to be our last activity/job before we are fully obsolete.
I can't think of anything that we won't be able to automate. Which brings quite a few questions in my mind in terms of how we'd be motivated to stay alive - working keeps lots of people off depression. But that's a different topic.
Do you have any thoughts on the topic?