My vote goes to Piltover/Zaun, too
Reasons:
1. We got alot of artwork for it.
Since you have to flesh out the region for the game completely, the amount of pictures we got with the lore updates will help you alot. Unlike other areas, we didn't just get some pictures of city districts, but even more in depth art like known devices from the city and the infrastructure (for example the lifts shown in the Warwick teaser, mentioned in the short stories, etc.)
Here an example of the hextech devices I mentioned.
http://universe-meeps.leagueoflegends.com/v1/assets/images/highlights/piltover-hextech.jpg
2. Most amount of cultural information.
Since we got an update for Piltover and Zaun, while both being subdistricts of pretty much the same big city, we got alot of information to work with. The short stories given to us showed, that the culture of these cities is pretty rich. We know about the Janna cult, some rituals like the Progress day (with pretty good description), we know about the cult of the Glorious Evolved. We got an insight about the political structure with the introduction of Camille and knowing about the Chembarons.
3. Trading City
We know that Piltover is a city trading with other nations all over the world. This is a great base for quests. Alot of people from different cultures are traveling this city, probably going to ask our "Champion" to do them a favor. At the same time, that means characters have a easy and logical way to travel to other nations.
4. Good introduction for a moral system.
I don't know if you had planned something like that. Let's say our character can achieve the ability to steal. Maybe the game wants to introduce some kind of moral system and including a mini-game for these acts. If you get caught stealing, you will get punished. Piltover is one of the few cities in the game, which actually have something like a police system (Piltovers Finest are proof of that). Meaning that the consequences for failing attempts to steal something can get punished in a less harmfull way. Other regions seem to mostly execute vigilantism.
5. Character Customization
Again, I don't know if this is planned. But since you mentioned the character customization, I would really love to be able to get augmentations and hextech equipment for my character. As shown in given art, Piltover also uses simpler body modification like dyeing hair, tattoos and piercings. I guess that this would attract alot of people.
6. Atmospheric diversity
Maybe that is just me, but I get the feeling that Piltover and Zaun provide the widest varity in atmosphere in Runeterra. We have the slums to discover, the houses of the people in charge of Piltover, the biospheres owned by chembarons in the depth of Zaun. All these things in just one big city.
Maybe to be continued (if you don't get annoyed by my WoTs ^^)
How and where would I like to start the game?
Since I already nailed down the region as Piltover/Zaun, obviously there. But even in this city, there are alot of possibilities how to start.
I would chose between 2 approaches, one for each subdistrict.
Piltover
If you didn't read the short story The Progress Day yet, I highly recommend to do so. It is fantastic and delivers a perfect hook to start our journey in this city. We could be a young scholar, trying to get a job in the big houses of Piltover at the Progress Day. It is perfect for a small tutorial (How do I pick up my invention and put it in the inventory? How do I use the map? How do I jump, interact with stuff, etc. to take shortcuts to not come too late?).
In my opinion, we should fail that first attempt, since otherwise that would mean our Champion is progressing too fast. The typical story, you sit together with your friend discussing how it went and you tell him that you failed. Meaning that you have to go back finding jobs people are willing to pay you for. Therefore, we start questing.
Zaun
Even in the stories, one aspect is mentioned pretty often, especially for young characters: gangs. Jinx, Vi, Ekko.... they all started in their own small gang. I think that could work pretty well for Zaun. We are a member of a small gang of people collecting junk and building their own stuff with it. You could give them a base, the tutorial would simply be to get out of your rooms and go to the base talking to the leader. He then proceeds to give you your first quests, like helping other members finding some specific components. Stuff like that.
End of your agony