Off the top of my head (and assuming arbitrary political/resource requisitioning powers) I might aim for Profoundly Self Sufficient Habitats.
This would basically be a kind of space exploration program on earth. The goal would be to develop a suite of technologies and practices to enable small groups of humans (less than 500) to survive and thrive with a technological civilization for centuries in extreme environments and cultural isolation. We should know how to build a habitat capable of supporting a group of humans generation over generation with construction of more habitat using ambient resources in (1) the Sahara, (2) the Antarctic, (3) deep underground, (4) at sea, (5) near Fukushima or Chernobyl, (6) at the top of Everest, (7) at the bottom of Lake Superior, (8) near deep sea vents, (9) in the upper atmosphere, etc.
You would need a bunch of new technology/culture and it would have to be relatively simple and self supporting, like 3D printers that can print their own components, highly efficient recycling systems, expertise in managing closed ecologies, cultural awareness of the dangers of culture loss/drift in small communities, etc, etc. This technology would probably have numerous spin-off applications in the rest of the world. The same project, assuming success, would create "life boats" that could hedge against certain kinds of X-risks. The same project would probably expand the effective carrying capacity of the Earth, because it would be opening up terrestrial niches for humans that we currently can't fill. The same project would be good practice for longer term goals like the colonization of the inner planets, the asteroids, and the Jovian moons.
.
I have just received a survey questionnaire regarding future directions in EU (European Union) research funding, and thought it would be interesting to see how LessWrong would answer the main question:
Imagine that EU funding is available for one ambitious, visionary project extending beyond 2020.