Transportation revolution, i.e. modification of the local gravitational field. Aka mass repulsion, gravitational shielding, antigravity, whatever we want to call it. One of the biggest blind-spots in science is that this is "impossible", or too far off to begin working on. My attitude is... self-driving cars, rocket-ships, etc are expressing the right sentiment, but are ultimately a misallocation of resources. Going to mars is thinking way too small, and has a small payoff. While gravity is a difficult problem to solve, I don't have to list out the potential benefits. What's better... a picture of pluto that took years and billions$, or a 3d printable craft that can travel faster than light and visit 10 different solar systems in 10 days. Almost nobody is working on it. Some places to start looking? Ultra-strong, ultra-high-frequency rotating magnetic fields (can be accomplished with stationary coils), plasma centrifuge or gyroscope, etc. Novel phenomenon in novel configurations under extreme conditions. I think the two most important steps are:
Cracking the code for room temperature superconductivity
Building a high-resolution, large volume (~10 x 10 meter) 3d printer that can print in multiple metals, plastic support materials, high-permeability magnetic core material, and most importantly, a superconducting material. Open it up for design submission, pick the best 20, and boom... we discover unexpected gravitational effects within the year, and fully master gravity within five years.
Once we build an AI, and we ask it for a way to circumvent the limitations of the speed of light, is it really going to say "i have absolutely nothing to contribute on the matter."? No, it will probably giggle and print out the instructions for 10 different methods. Then again, since it would be so darn easy for AI, maybe we should just hold off on gravity research until we have AI, then let it do all the heavy lifting :)
"There is no such thing as science-fiction technology... only science to which we have not yet sufficiently applied ourselves." -Bob