First things first - get those civics changed
Talk to a really undeveloped civ like Mali or the Inca. Chances are you'll have lots of techs they don't have. Trade one of them (in a lot of my games I can trade something really old like philosophy or economics) for the world map - this will tell you who the movers and shakers are, and also tell you who owns what in the Americas.
Hopefully you'll start at war with the power that possessed New York (as soon as that city flips). This will give you extra troops and as BED said, some of their troops will disappear. Taking the copper deposit north of New York quickly is paramount to our UHV. Without it, building the statue of liberty first will not be an easy task.
I find in my games as the USA in the first few turns I am churning out workers to get the central United States developed as quickly as possible. We want Denver, Chicago and New Orleans up and running immediately. Denver's production capability is nothing short of monstrous.
For cities, the places I found I liked the most as USA are:
- Washington
- New York
- Miami (southern tip of Florida)
- Toronto (or Fort Albany/Fort Rupert - Fort Rupert is a favourite, it is on the river, one tile West of the copper)
- Chicago (between the two corn resources)
- New Orleans (North of the fish)
- Denver (directly on the oil)
- Vancouver (Northwest of the marble)
- Los Angeles (South of the cow)
- Reno (settle this one last, and make sure there already is a farm on the rice, and a camp at the deer since otherwise there's no food. This is a good city to get the precious metals East of Vancouver. The spot we should settle here is one tile East of the rice)
If we want to conquer or build more, or maybe try to mimic the USA today, other possibilities include:
- Pearl Harbor
- Anchorage (on the South coast of Alaska. Unfortunately you can only settle directly on the deer, as far as I am aware)
- Saskatoon (In the forests north of Denver. Build it on a river and so it will encompass the oil, deer, and as much forest as possible. If you plan on building the National Park wonder, make sure it is here. You can get a LOT of free specialists by making forest preserves here)
If I am playing single player, I raze all other cities, or if they flipped to me I go into worldbuilder and remove them (such as Boston/Popham/Jacksonville). I don't know if you'd consider it cheating
At some point you'll want to start thinking about those sexy oil deposits. We have quite a few near home:
- Northern Alaska
- Saskatoon has an oil deposit
- Denver
- New Orleans
- Gulf of Mexico
Next we'll want to start stealing some oil. Fun places to strike include:
- Caracas (you will likely have to declare war on Spain at some point to kick them out of the Caribbean or Mexico. Why not take their oil, too?)
- Lagos (if someone has settled here, or even if no one has, you could always make yourself at home
)
- South-West Norway (if the Vikings collapse, we may as well take the easy oil deposit just off their shores)
- Arabia (If we take Baghdad and either settle or capture Kuwait City, we can take over 2 or 3 deposits in one go. Other cities to strike or found include Dubai and Masqat)
- Brunei City (If no one has settled here... we could always invite ourselves in
)
