I wonder what the game background for this game is going to be.
If I may make some suggestions, how about two for now?
The first one is set right after Fallout 1. The Master has just been defeated, the Vats have been destroyed, and leaderless Super Mutants are now searching for a new goal to live for while the settlements in the Core region are dealing with changes the Vault Dweller has brought.
During this time there could also be focus on the Mojave region which was still mostly tribal (the same goes for for Arizona).
Around this time New Jerusalem or Jericho/New Canaan has probably appeared by now and I think Vault City is also around.
The second setting would be after Fallout New Vegas, dealing with the aftermath of the actions and decisions the courier made during the game and who he or she supported.
The Core Region would be available, as would the Mojave, Nevada, Utah, and perhaps Arizona, New Mexico and Colorado.
I have a few ideas for this suggestion myself but as this is a team effort I think others should have their voice heard as well.
What I would like to do.
* The Brotherhood of Steel got wiped out on the West Coast. During the BOS-NCR war the NCR army came to close to Lost Hills to the liking of the paranoid BOS Elders and they chose to blow up the bunker rather than let it and its technological secrets fall in the hands of of the NCR.
There were BOS survivors, some managed to reach other chapters and bunkers while others went 'native' and gave up their old lives.
Hidden Valley is currently the new headquarters of the Brotherhood and an unease peace exists between it and the NCR. Time will tell it Mcnamara and the new council of Elders will make the peace lasting or that the remaining warhawks will get their wish and start a final war against the NCR.
* The NCR managed to secure Hoover Dam during the second battle of Hoover Dam but failed in annexing Vault City which is now completely independent after the reactor under the Lucky 38 was turned on. It is still being run by Mr House but it is unclear if this is the real Mr House or Yes Man posing as Mr House.
NCR has since then started to build its own settlement around Hoover Dam but it lacks the glamor and riches of New Vegas which the NCR still envies.
* Caesar's Legion has been driven Eastwards and the NCR has been sending armies into New Mexico to harass the Legion and gain allies.
It is not as welcomed by the natives as it expected to be as the disappearance of the Legion has given rise to new raider gangs or reappearance of old gangs that went underground.
I would leave it vague if Caesar or Legate Lanius were killed during the second battle of Hoover Dam.
* The Diablo Canyon Nuclear Power Plant, once the headquarters of the Union of Atomic Workers has been discovered. Recovered records once made and guarded by the Union details the design and working of nuclear power plants. (the BOS wasn't happy when this technology was rediscovered by outsiders)
* Prospectors from the Boneyard have started salvage operations in the ruins of Vandenberg, recovering advanced technology including rocket technology such as the star clipper space plane that could be made operational again. (another sore point to the BOS who wanted to keep this place out the hands of ignorant wastelanders)
* Naval Air Weapons Station China Lake has been discovered. Much to the relief of the BOS elders no one has been able to enter the ruins of the base and bring back some of the advanced weapons that were being developed and tested here though evidence indicates both regular wastelanders, Ghouls, and even some of the Unity's patrols have tried only to be cut down by the base's automated defense systems.
During the BOS-NCR war both sides tried to secure this facility and its resources for their war effort but neither of the succeeded, Brotherhood squads consisting of Paladins, Knights, and Scribes, and NCR platoons sent to the facility have disappeared without a trace.
There are rumors going on that the place might be a holdout of the Enclave.
* NCR has made contact with Fort Abandon again whose population has mostly survived the occupation by Caesar's Legion. They are however not interested in rejoining the NCR.
* The NCR has reached Denver and established a headquarters in the city's central train station. The troops stationed here now watch over the rail lines that run back all the way to the West Coast.
They were fixed with the help from the Iron Rivers tribe who has maintained the train engineering knowledge of some of their ancestors.
A train travels between Hoover Dam and Denver once a month, bringing supplies, fresh personnel, and travelers and adventurers that seek to make their fortune in the pre war city and its surroundings.
NCR has also established a prison in Denver, sending prisoners there as part of a work release program.
* The first signs of the projected famine foreseen by the Office of Science and Industry are showing, causing unrest in the Core Region.
Combined with the unrest that followed the Mojave campaign revolutionary movements have been forming within the NCR. The NCR fears a possible civil war or revolution if this anti establishment movement is allowed to continue.
* The Khans have fled into the planes of Wyoming and together with members of the Followers of the Apocalypse have formed the Khanate, a powerful empire that rules much of the land there.
Though currently not aggressive towards the NCR the Khanate has made it clear that the NCR's settlers are not welcome here.
The NCR government sees the Khanate as a possible threat to the Republic and want to mobilize the army against them.
(heh, this one should probably be ignored as I personally do not consider Fallout 4 canon in any way but I could not resist
)
* Travelers and frontier patrol mention sightings of strange artificial men called Synths at the frontier.
It has both the NCR and BOS leaderships worried. Has another army woken up in the Wasteland?