How about a faction of Chinese Remnants or Communist supporters? Or would that be too cliche?
Like for example, a large spec ops team was sent into the US to (...do something...). However the next week the war came. The spec ops team resorted into a high tech bunker outside of a city, say Chicago or something, that they had built. From there, the small spec ops team grew into a huge society. Sooner or later that society emerged from their underground bunker to find the wasteland world around Chicago.
So they make plans to dominate the wasteland. They have the manpower, and the technology (they not only have the most advanced Chinese military tech, but they have also recently raided an abandoned US military base that was loaded with supplies and military tech).
So now they operate out of this huge military base, they have power armor suits, energy weapons, and perhaps even a small fleet of Vertibirds (its kind of like the anti-Enclave). Not only that, but to give them more manpower they are taking on new recruits (and training them military style like the BoS).
This faction would be ruled by a man called "The Chairman" (as opposed to the Enclave in FO2 which was ran by "The President"). The Chairman would also have a "People's Congress" set up to. Their goal is to carry on the communist domination of the US even after the war.
These are the main enemies. As you get deeper into the story line, you find out a darker plot, and the real reasoning behind them being in the US in the first place.
But for now, when you emerge into the Wasteland world in the Fallout game, the first town you come across is a town that has been taken over by these Chinese Remnants. They operate under a Communist system. All the residents of the town are forced to work, live together in buildings, and line up at a Chinese Remant office every day to receive a fair ration of supplies. No one is happy about being force to work under this system, however no one dare speak about it.
The character talks to many people in the town, and after enough investigation finds out about a resistance group fighting the Chinese Remnants and attempting to bring freedom to the Wasteland. So you meet with a Resistance member who has a plan going to retake the town from the Chinese Remnants. You execute his plan, which leads to an eventual bloody battle between the Resistance and the Remnants right in the center of the town.
The Resistance members fight through the Chinese Remnants (who have more manpower, AND much superior technology). The Resistance eventually destroy the Chinese Remnants in the town. Just as they celebrate, thinking the battle is over, a Vertibird flies in to drop off a whole new batch of power armored reinforcements. It seems like the battle is over, as the Resistance members know once those power armor clad soldiers reach the ground the battle is over. However, in the last moment, a resistance member is seen climbing a building with a Fat Man. He launches the mini nuke at the Vertibird, destroying the Vertibird and the entire power armor detachment of Chinese Remnants inside.
As they people of the town celebrate their victory, your character decides to move on, for he must continue searching for (whatever it is he is supposed to be looking for). However, once the characters travels the wasteland, he finds a terrible reality. The Chinese Remnants have captured half the towns of the Chicago Wasteland. He also finds several Resistance members fighting a losing war against the Remnants, with several small skirmishes happening throughout the outskirts of Chicago. He continues on into Chicago, the ruins of a huge city with enormous buildings, but also terrible bands of raiders and mutated creatures inside those ruins. He then finds a huge society living right in the center of Chicago. It is the largest, most spectacular town the wasteland has ever seen. Even more, he finds out that the Resistance members are the ones who are in charge of the town. He discovers a name for the Resistance (something catchy).
Anyways, the player goes on to find what he was looking for. However he can't turn his back on the Chicago wasteland and its people, which he knows will eventually be conquered by the powerful Chinese Remnants. So a drastic and climatic story line ensues. The player takes towns back from the Chinese Remnants with the Resistance town by town. However, they find it to be to no avail, for every town they take back, the Chinese Remnants capture two more. So the Resistance hatch a plan. They figure that the only way to destroy and stop the Chinese Remnants is to destroy the military base they are headquartered on.
However, this military base is heavily guarded, and equipped with some of the most powerful technology built by the US and China. So they send in the player undercover, pretending to be a "new recruit" to the Chinese Remnants. Here the Chinese Remnants teach the player how to use, and gives them power armor (T-51b model). After investigating through the base, the player finds a restricted level. He sneaks (or fights, or maybe talks) his way through the restricted levels, to find the Chinese Remnants harboring a full nuclear tipped ICBM.
When the war happened, something happened in the mechanism, and the weapon didn't fire. The Chinese Remnants however have replaced the firing mechanism and fixed it. As you attempt to detonate it under the underground base, you are stopped by the leader of the Chinese Remnants himself, the Chairman.
He sounds just like the Enclave President in FO2. He tells you how what they are doing is going to bring peace and unite the wasteland. He tells you that he has grown to love America, and does not wish to see it destroyed. However he also believes so long as the Wasteland is how it is (separated, un-united, tribes of raiders killing, stealing, mutants throughout the wasteland), the American Wasteland will not last long, and will once again destroy itself.
He also lets you in on two dark secrets.
1) The Chairman was planning to launch the nuke unto Chicago to destroy the Resistance. He states that he doesn't do this, the Resistance will stop the Chinese Remnants, which will ultimately lead to the destruction of post-war America all over again.
2) The Chinese Remnants Spec-Op team that was sent before the war, was actually sent to wait for the nuclear apocalypse. The Chinese hatched a plan to start a world-wide nuclear war. They would send a military team to america to wait for the nuclear war. After the nuclear war would come, they would use the post-apocalyptic weakened america to their advantage to take over America.
However the Chairman has grown to love America. Instead of destroying it/conquering it under a PROC flag like his initial orders stated, he is going to unite it under his own communist system. He believes that by doing this, not only is he "saving" post-war America, but he is giving the land back to the people, and letting the people have a government that is truly "by the people, for the people".
You can talk him out of his plan, kill him and his person guard, or simply detonate the nuke under the military base.
Either way, the player character destroys the Chinese Remnants. However in the ending cinematic, it is discovered that he could not escape the extremely large underground base in time, and succumbed into the nuclear fire.
However, his noble actions saved the wasteland from yet another villain with a strange and large plan and personality.