I would probably play a few different simulation games like Civilization and try to optimize society based on the best parts of each civilization in history.
Might even separate areas to experiment with different ideas example China and Hong Kong two systems but one country but pushed further to one specializing in avionics and space development the other country agriculture and deep seafaring technologies.
Try different legal procedures and different laws within countries such as difference between Civil and Common Law or Even Sharia and develop a system based on all three but using the best of it.
And have fun with society set minimum working age in different countries one 10 one 12 one 14 one 16 one 18
Same with consent and marriage
Then try different types of education systems classic example focus on math in asian countries focus on general arts and creative thinking in Western countries
Play with subsidization in some countries and remove it in others and see how people adapt and where they become the most creative since the brain is more malleable when young does it make sense to be innovative at a younger age and have people learn at older ages or is it better for education to be taught as it is and for the big wigs and corporate structure to be old and unchanging slow to innovate.
Goes into environmental structure so developing the right structure is worth a reanalysis to find and discover the best optimization settings.
Then Try developing a tech paradise in one city and an ecological efficient sustainable city in another.
Rebuild the internet make a mesh-net that uses computing power to try and develop plasma based engines and do formulas that would take significant man time but can be replaced with processing, aka organize big datasets into something useful like is being done with medical research
Replace oil energy with geothermal energy in the long run with solar becoming more efficient and using less energy in the production process
First by sticking rods around Volcanos then finding better processes to acquire the earths internal core temperature
Then using magnetic fields try to utilize that energy into a low density field to store energy since our current systems are limited by live current basically we can't store energy in signifcant amounts to solve that we need to concentrate energy for long durations of time. (Hard light) etc.
Develop new storage systems using DNA sequences to maximize the writing of data
Overall resulting in a bit of a mad scientist as I try to develop cryogenics in my quest for immortality and then creating an interactive virtual world that allows time to pass by faster in it than outside it example 1000 hours in VR is 1 day in reality allowing for more time to develop the outside society within a single human lifetime.
Oh some of this exists already but making scale and improving it is the goal
http://gameslikefinder.com/games-like-civilization/http://en.wikipedia.org/wiki/Superconducting_magnetic_energy_storagehttp://en.wikipedia.org/wiki/List_of_national_legal_systemshttp://en.wikipedia.org/wiki/Malleability_of_intelligencewww.reed.edu/~mab/papers/fletcher.ab96.pdfhttp://en.wikipedia.org/wiki/Person%E2%80%93environment_fithttp://en.wikipedia.org/wiki/List_of_distributed_computing_projectshttp://en.wikipedia.org/wiki/Geothermal_energyhttp://en.wikipedia.org/wiki/Big_datahttp://en.wikipedia.org/wiki/DNA_digital_data_storagehttp://accelworld.wikia.com/wiki/Brain_Burstwww.shs.edu.tw/works/essay/2006/10/2006102810584206.pdf