Where are you visiting from? Don't think that NYC is like the rest of this country. It isn't. There is a lot to see and experience here. A lot depends on how much time and money you have for this visit. Vancouver is nice but it is in Canada. Mexico and Mexico City have a lot to offer too.
PM me and I'll tell you how to easily avoid the slums and likely problems.
Mexico City is in Mexico- Watch your purse, it's very crowded and dirty
Vancouver, Washington or Vancouver ,British Columbia?
New York-Times square, Statue of Liberty and the 9/11memorial are a must see, if you like shopping you will LOVE NYC.
Suggestions that aren't on your list- Grand Canyon -Charleston, SC, Washington DC, San Francisco
Buy a gun before you go for protection.
Hostels are not especially popular or available in the US. They are more of a European thing. There are only a very few of them in the USA.
I am not especially familiar with any of the cities you mention, but all cities have slums - full of gang members, drugs, crime, hookers.... you'd do well to stay out of those. They are usually near the center of the city, not on the outskirts like in European cities.
Mexico City is in Mexico. It is not in the USA.
LAX is airport in Los Angeles.
I have lived in America for 45 years but have not visited any of those places. Sorry. Good luck to you dear!
West coast. I hope you find some good traveling advice. The only thing I know about Honolulu is that one must pay for water in restaurants
Who said California is not a state? I can assure you that it is.... Anyway, going to bed now.