Going through the Beta Site champion pages, plus a few of harrow's post (about multi-allegiances champions and about Sion's origin) I made a list about the Factions and it's champions:

About the factions:
There are currently 12 factions, plus the Independents.
Demacia, Noxus, Zaun, Piltover, Bandle City, Bilgewater, Ionia, Freljord being the City States recognized by the league.
Mt. Targon, Shadow Isles, Shurima and The Void being places where there weren't any cities, or are another dimension or something.

• I can't see Mt. Targon going for the City State status, too warlike, and the Solari too few.
• Shurima could have survivors, but Ezreal in Aatrox teasers said that there wasn't anything there.
• Shadow Isles could move politicaly and get recognition, but it wasn't stated in the Shadow Isles patch.
• The Void is the void, they don't realy care about politics and stuff, they do Void-stuff.

• Fiora, Galio, Garen, Jarvan IV, Lux, Quinn, Shyvana, Vayne: Prety straightforward Demacian, all known, some of them like to shout their country's name around
• Poppy: She has ties with Bandle City.
• Sona: Is native Ionian, but is only listed as Demacian
• Taric And Kayle: Are Aliens, directly related to the league, why is he Demacian now?
• Xin Zhao: Now is listed as Ionian, well, he could hail from there, as it makes sense as he looks asian, and he had to be from somewhere before the Fleshing. We'll see.

• Darius, Draven, Katarina, LeBlanc, Swain, Talon, Vladimir, Cassiopeia: Standar Noxian fare, likes to kill stuff, some are part of a knife nut family, others part of a secret society of ancient secrets and magic, I guess that this could be added as a faction.
• Morgana: Alien with ties (if by ties you mean a Bakery) to Noxus. Is stated to be more independient.
• Urgot, Sion: Noxian warriors to the death and beyond, linked to Zaun, as in Urgot's case his rebirth was there, Urgot's link is listed as an error, let's see what's going to happen.
• Riven: Embraces Noxian ideals, but right now is opposed to it's leadership, I would list her as Independent.

• Blitzcrank, Twitch,Viktor,Zac: The general Zaunite, pretty diverse crowd, even though politicaly they are mostly independient, Blitz more to the league and Viktor to the GLORIOUS EVOLUTION but could work under Zaun. Zac and Twitch are more related to the city.
• Dr. Mundo,Singed,Warwick: They in some point were stated as noxus allies, does this still stand?
• Sion,Urgot: See Noxus

• Caitlyn, Ezreal,Jayce,Orianna,Vi: The peacemakers, the inventors, the invention and the archeologist. Orianna might seem the odd one out, but if she holds her father's and her.. namesake's wishes, she'll fight for Piltover.
• Corki,Heimerdinger: Shouldn't Ziggs be here as well?
• Zilean: What? He should be Independent (As Uristan only survivor, it doesn't need mediation), or tied to the league after the Kalamanda incident. I would see him in the Shurima crowd before here.

• Ziggs,Rumble,Teemo,Tristana: The Yordles with the interest of Bandle City at heart... are not many. Ziggs should be tied to Piltover as well, I think
• Corki, Heimerdinger, Kennen,Poppy: This is why Rumble feels the need to be a nationalist, too many Yordles are loyal to somewhere else before Bandle City.
• Amumu: I guess nominaly is a Bandle City champion, but there's nothing there for him he isn't even being driven mad by the issolation, should be either independient or tied with Shurima.
• Lulu, Veigar: Even if this is their birthplace, their morals don't align with it and don't care about it, they should be both independient.

continued

Bilgewater:

• Fizz, Gangplank, Miss Fortune: True ties to the Island of Pirates. YAR!
• Graves: Born there, but made it big in the land, should be independient.
• Nautilus: No ties, only place of resurfacing, should be independient.
• Twisted Fate: No ties, should be independient.

• Irelia,Karma,Lee Sin,Master Yi,Soraka,Wukong: The people (and monkey, and goat ex-goddess) that seek true balance. Ionian souls.
• Akali,Shen,Kennen: The ones that actualy enforce balance, the call of the Kinkou should come before any other.
• Xin Zhao,Udyr: Born here, loyal to Demacia, Trained here, Freljordian by Birth. Sona should be here as well, but she wasn't listed.
• Syndra,Varus,Zed: Neutral at best, looking for the downfall of the island at worst, they don't bring balance, either by Vengance or thirst for power. Should be independinent
• Ahri: Her origin story makes me think independient, but if she wants to be human, then alleigance to her birthplace is a start.
• Jax: I.. don't even... Jax Ionian? Jax should be an independant misterious being, who either turns out to be related to Aatrox or the missing high counsilor of the league. What's the story about this one?

• Anivia,Ashe,Gragas,Nunu,Tryndamere: The Avarosan, following the path of peace and building an economy and a traditional country.
• Lissandra,Trundle: The Frost Guard, using subterfuge and deception, looking for the chance to bring back the powerful Watchers and make her followers Iceborn again, or to club out an old witch and take the north for the trolls.
• Olaf,Sejuani,Udyr,Volibear: The Winter's Claw, either seeking balance with nature, or a warriors path, or both, surviving the cold through might.

• Diana,Leona,Pantheon: As far as objectives go, they are too disperse to be considered one faction, the only thing that they have in common is their birthplace. They are Targonians but that can't be considered a faction.

• Rammus,Xerath: The only ones that (currently) were born there, but one is Ok with it, and the other doesn't care. What is in Shurima that people should align with it? I'd say that they are both independient, but let's see what is in stores for the south.
• Nasus,Renekton: At least Nasus seems to be interested in the site. They are currently both aliens from the same world, but Renekton is a prissioner of the league.
• Cassiopeia: Noxian, but her relation to here might sheed some light about her curse
• Sivir,Skarner: No idea, both are independient in their current lore, let's see what happens. I hope that the aspect of the "Crystal Vanguard" and Kalamanda's ties don't get lost.

• Elise, Evelynn, Hecarim, Karthus, Mordekaiser, Tresh, Yorick: All misterious being who seem to work for the same purpose but with wildly different methods. Different ranks, different reactions from the altar lords, but not enough information to say anything else.

• Cho'Gath,Kha'Zix,Kog'Maw: voidborn creatures, each one with it's own purpose, but all share a hunger for that world. Though two of them are prissioners of the league, they are Void agents first.
• Malzahar: The void prophet, not much to talk here.
• Kassadin: Listed as part of the void, but is working directly against it. Should be Independient.

• The rogue mages: Independient spellcasters that as far as we know are free agents: Annie, Ryze, Janna
• The Nightmares: beings from beyond human comprenhension, the league manages to subdue a few of them, but they still are looking for ways to fulfill their destiny, or saciate their thirst for blood: Brand, Fiddlesticks, Nocturne, Shaco
• The elementals: beings that can't be clasified as animals, as their makeup is either vegetal or mineral: Zyra, Malphite, Maokai
• Miscelanious races: a little despective, and a little deceptive, but as the last group, that aren't aligned with their races, and have no city to call their own, or if they do, it's outside the league's range: Alistar, Nami, Nidalee, Rengar