I almost posted this question in /r/AskAcademia but I figured I'd try here first. I'm exploring graduate programs in history and while I'm generally interested in all history, I am curious, what time periods and/or regional areas of historical research might have more room for advancing the field of history? Thanks.
To be entirely honest, your chances of finding gainful employment after graduate school are so profoundly slim, you might as well study whatever esoteric subject or region excites you most.
That said, there are a couple ways to answer this question: What's hot? What's understudied? The two are not entirely synonymous, and you'll probably get different answers from different academics. Either way, I'm ideologically and intellectually opposed to the notion that anything can be over-studied. The entire idea of the humanities is that humans and their texts are interesting and that other humans, by reading them, can find new interpretive fruits from their own unique engagement. Shakespeare has been written about hundreds of thousands of times or more, but I'm entirely confident that your reading of Othello will look different to mine--and I want to know your take.
So, with that out of the way: what's hot? According to AHA data, if you want a tenure track job, you're at a slight disadvatage if you study North America. Middle East is, for obvious, State Dept. funded reasons, a good choice. If you do study the US or Europe, a second field in a non-western area will allow you to go after "...and the World" jobs. Thematically speaking, I've seen a lot of job announcements asking for history of medicine and environmental history, so I suppose those are still "hot." Digitial humanities is a boon if you know how to code. Historians are super impressed by rudimentary GIS skills. It's a handy set of tools, regardless.
What's understudied? For structural reasons, these are often NOT the fields you want to go into, since there are not many jobs. How many chairs are there in Pacific history outside of Australia/NZ? African history remains terribly unrepresented in history faculty. There are often multiple professors of German, French, British, and Russian history in a dept, and exactly one person to handle the whole of a continent. The history of sexuality, especially in non-western contexts, seems like a relative lacuna.
But none of that matters! Follow your passion. I hope you get a good job at the end of it, but the odds are literally such that you probably won't. Instead, get a funded PhD program and enjoy your five to seven years of interesting reading, conversation, travel and work.
Good luck!