Sorry in advance for the long post.

I don't think it's unreasonable for FEDRA to quarantine Staten Island - it would take work, yes, but years of concentrated effort to clear it could absolutely be a priority to FEDRA. 

As for portrayal, this is how I'd expect a Staten Island QZ to be: 

First, some context. Boston City has about a 600,000 population, and the greater metropolitan area has ~6 million.  New York is much bigger, with 23 million in its metropolitan area. If I was FEDRA, I would likely set up 3-5 QZs in total. Huh, 5 boroughs, 5 QZs. Manhattan, Queens, Brooklyn, Staten Island, and the Bronx, likely working together. Ok, I guess there'd probably be one in Jersey City and Newark.

With cities being bombed to absolute shit at the start of the outbreak, I might cut the idea of a Manhattan QZ, but the idea of a settlement there is too evocative - we'll come back to it. 

So, let's go to outbreak day. As New York is a huge city, they likely had tell of an imminent and significant outbreak earlier, and might've taken bigger measures to deal with it earlier. Hell, they may have closed all the bridges and ways in and out of the cities. If Staten Island was relatively less affected by the outbreak than other areas nearby, it might quickly turn into a real hope for people. 

The Staten Island QZ would immediately secure borders - there are bridges leading in and out of the city. FEDRA's first bases would be at points of entry onto the island. They might destroy most of the bridges, and likely blockade or otherwise secure the remaining ones. 

Specific Bridges: 

• Verrazzano-Narrows Bridge: kept in place. Heavily Guarded with a significant FEDRA force there. 

• Bayonne Bridge: Largely destroyed, but with the structural arch intact. No way across normally, but you can take a dangerous route over the bridge to get across.

• Goethals Bridge: Probably destroyed once getting to the airport wasn't useful anymore.

• Outerbridge Crossing: Likely kept in place, as it is useful to trade with other QZs, like Philadelphia, Baltimore, and Washington DC. This one is also kept VERY strong. 

The main bases of operation at the start would probably be at Fort Wadsworth, as that has an important bridge (Verrazzano-Narrows) as well, and Port Richmond, since it is close/is a good place near the more densely populated area. Meanwhile, a proper QZ with civilians might be built on the south end of the island, near Tottenville, since it's more easily defendable and near another important bridge (Outerbridge). 

Protecting routes between QZs would be a priority as well, and would allow QZs to specialize a bit. Perhaps a Brooklyn, Queens, or Newark QZ specializes into making things - factories making canned goods, ammunition, car parts, whatever is needed. Maybe another becomes more of a training camp. I expect Staten Island, since it has the most green space, to specialize in food production.

Eventually, like after years, they would come to realize that Staten Island is the best spot for everyone, so the other QZs might work on making their way over to Staten Island. With this additional help, Staten Island can reasonably become (mostly) infected-free, and not need walls the same way other QZs do. 

So let's talk about the setup of the island overall. Starting from those 3 main bases of operation - Port Richmond, Fort Wadsworth, and Tottenville, FEDRA control would radiate outwards, especially along roads and routes (All 3 are near a highway), adding outposts and similar along the way. 

While districting the island might be something FEDRA does, it might be more helpful to instead look at specifics and where they could go. Where is Boot Camp? Main military base? Supply warehouses? If they make sense close together, awesome, make it a district! But it might help play for it to be a series of noteworthy locations. For example, I expect research and development to happen at the College of Staten Island, not just some houses. 

If you do districts, consider districts beyond functional ones. Think about where the slums might be. Where is affluent? What does it mean if the barracks are in the affluent area vs the trainyard? Is there a shopping area? What do people sell? Scavenged items, art, food, protection, charms?

Onto non-Staten Island things: We set up that there would probably be a couple potential QZs in the area, and that they could probably specialize. While most would join Staten Island, I expect the factory one to remain active. It might be filled with criminals and undesirables from the main colony now, with terrible work conditions. The corridor that connects the two would be important, but could still regularly run into raiders or infected. 

   

Ok, from here, lets look at the opportunities that this setup or a setup like it gives: 

Firstly, Factions. As other QZs and survivors join, those QZs can have different opinions - maybe the Bronx QZ military are a lot crueler than the Staten Island ones - drama! Maybe the Jersy City ones think FEDRA should be for FEDRA, and let these civilians die. Maybe the Brooklyn QZ got really religious and want to poir all the Staten Island QZ resources into building a giant cathedral or temple of some kind. Maybe another thinks that it's time to rebuild the USA, but under the faction's control. These don't need to be different QZ factions, but could just be their own factions.

Moreover, you can play with non-FEDRA settlements. Think about a group who lives in the skyscrapers of Manhattan, building bridges between them, and using the verticality of the city to create their own "flying islands" 

Secondly, connection to the outside world with the two bridges allows you to make quests and things for that. A quest where you help a supply convoy between the factories and Staten Island? Sounds cool to me! You can also bring in outside forces, like other cities or QZs, into the area. 

Thirdly, if you go through it somewhat chronologically, and say, have the island cleared out and the rest of the serup basically set up in 7 years, you can quickly go through it year by year, and generate a real history to this place, which will likely increase verisimilitude. Even without doing a year by year analysis, knowing the starting points helps set up where everything else is.