Since Justin S. Davis posted his 22 quick questions for your post apocalyptic campaign setting (referencing the classic Twenty Quick Questions for your Campaign Setting) I've been inspired to come up with my own version. (Sorry Justin, but your 22 questions just didn't completely feel right to me, though they are inspirational, heck maybe even Sniderman and Brutorz Bill will come up with their own versions).
20 Questions for your Post Apocalyptic Setting
1. What is the deal with this cult/gang/cryptic alliance?
2. Where can we go to buy equipment?
3. Where can I get a vehicle or monstrous mutant mount?
4. Who is the mightiest robot in the wasteland? (or wizard/sorcerer for more Thundarr-like settings)?
5. Who is the greatest warlord in the wasteland?
6. Who is the richest person in the wasteland and what are the major forms of currency?
7. Where can we get high-tech healing?
8. Where can we go to get cures for the following conditions: poison/toxin, disease/infection, radiation poisoning, disadvantageous mutations, nanobot infestation, corrupted databanks, broken cybernetic implants, broken robotic parts?
9. Are there cults/gangs/cryptic alliances I can join and/or fight?
10. Where can I find a loremaster, technician, or other expert NPC?
11. Where can I hire mercenaries?
12. Is there any place on the map where mutants/humans are outlawed/hunted or other notable hassles for PCs?
13. Which way to the nearest bar, brothel, dive, or hive of scum and villainy?
14. What threats are terrorizing the wasteland sufficiently that if I kill them I will become famous?
15. Are there any wars brewing I could go fight?
16. How about gladiatorial arenas with fabulous prizes?
17. Where is the nearest contaminated zone?
18. What is there to eat around here?
19. Are there any legendary lost vaults/laboratories/military installations/shopping places around?
20. Where are the nearest scavengeable ruins?
Special Bonus Questions for more hard-core survival oriented settings:
21. What is the most common source of fuel/power and where can I get it?
22. Where is the nearest source of clean water and who controls it?
23. Is it safe to eat that food?
24. Where can we get ammunition for these weapons?
25. Where is it safe to sleep?