There is still so much to do. Currency is a big thing. Me? I'd head to the Federal Reserve or Fort Knox or wherever we keep our gold, silver and platinum and secure it and probably bring it to St. Louis for safeguarding and restart our currency tied to gold. A new White House needs to be found. Cabinet members need to be named. Elected officials and elections! I would also head back to DC and get the Constitution and bring it back. Same with other important documents in the archives. I'd secure the Pentagon and any tech and info there that might be necessary. Same with NORAD.
If they seriously can't get into that bunker in the White House I think it needs to be destroyed. The same with the Pentagon. First off it is too big of a symbol to let it remain there for some warlord to declare himself the President and move in. Second having those rotting bodies inside? Gross.
The free world has only one ship, The Nathan James, in dry dock undergoing repairs to protect it from rogue groups. Teams need to be sent out to find other working ships and crews must be trained. Fire and Police must be trained and put to use. Communications have to be reestablished. Hospitals, doctors, nurses, judges etc...
It might even be beneficial to try to get the population of the US to move to the midwest and St. Louis. At least until the US Government is firmly established. Then people can be sent back out to the other cities complete with trained police, fire, doctors, nurses to repopulate those cities. And it also makes it more likely that everyone will have received the vaccine/cure.
One ship isn't going to be enough to take on whatever obstacles are out there in the rest of our country much less the rest of the world. They can't cure the rest of the world without encountering just as many problems as they did curing this small portion of the US. There will still be some who want to control the cure in their countries and cities, or even destroy it.
So no I don't think the show is done. I'm glad there will be a third season and hopefully more after that. Their initial mission is complete yes. But that doesn't mean they are done. Just because the cure has been found doesn't mean the world is all better. It is a mess and someone needs to start fixing it. Unfortunately the crew of The Nathan James is the only military and pseudo police force that exists right now. Their job is far from done.