I think an interesting direction is figuring out how to leverage web tech (or just code in general) to interact with the real world. Consider companies like Uber and AirBNB. They've identified a real-world problem and set out to solve it using technology. A lot of the "cutting edge" stuff these days is figuring out how to take a real-world problem (genetics, taxis, mail), and writing some code to make it accessible, cheap, and easy to do.
The problem with "cutting edge" is that it's often ahead of its time. It takes a LOT of time and effort to make even a tiny dent in the space of "cutting edge." If that's something you want to do, you might want to go back to academia and stay there. The "real world" is a bit more pragmatic -- there's a reason the space shuttles tended to have tech from 20 years ago and not brand-new tech from last month.
IMO to find interesting projects, a better idea is to look backward: what industries are still in the 20th century, and how can you help bring them into the 21st with modern technological advancements?
What about farmers, truck drivers, construction workers? Why are they still driving tractors, trucks and bulldozers? Why aren't robots doing those things more widely?
What about real estate agents and their legalese? Why are real estate agents still handing me stacks of paperwork? Can't you Zenefits the crap out of that process?
What about community outreach programs and community centers? Why are community outreach programs still accosting me on the street and handing out fliers? Can't they do outreach digitally? Can't we automate scheduling basketball games and pick-up kickball games?
What about having to fill out paper applications or stand in line at the DMV? (Shouldn't all that crap be automated by now?)
What about having to actually hand your credit card to the cashier at the drive-thru at McDonald's? (Can't they just magically detect who I am somehow and charge me accordingly? Why do I have to hand some punk ass kid my card or cash?)
What about planning weddings or raising kids? (Haven't enough people gotten married that planning a wedding should be as simple as browsing Amazon for a few hours? Haven't enough people had kids that we should have some solid data about what works and doesn't work?) (These two things aren't really tech-related, but man, if you could figure those out...)
The best part about this approach is that pretty much any idea you come up with will be "cutting edge" as far as these areas are concerned. These are the things we're still doing the same way we did 50 years ago, before computers were even a thing.