Don't let the In-N-Out propaganda machine fool you! Their burgers are just ordinary.

Well, in my opinion anyway.

I don't know how different Mexican food is from Brazilian food, but LA has a ton of good Mexican restaurants...or at least I'm told. I wish I could give some suggestions. You should look into attending a taping of a sitcom (or another kind of show) or something. Tickets are free, but be sure to arrive early, and I would only advise this if you have like 6 hours to kill. I think this is the website I used for The Pink House ticket, but I'm not sure:
http://www.tvtix.com/ You can get tickets for both LA and NY.
When you're in NY, you should probably visit the statue of liberty. People can still do that, right?

I've never been to NY, but I know Coney Island is famous...is that place still up and running?
As for food...According to the travel channel, Nathan's Hot Dogs in NY is supposed to be ~the best hot dog in the country~, but then they say the same for Pink's Famous in LA (which I've had), where the hot dogs are named after celebrities, and they randomly assign you a celebrity when you order(I was Megan Fox

). I only mention this since hot dogs are an iconic American food, but I'm sure there are much better dining options available. The pizza in NY is also supposed to be really good. Perhaps Sal or someone else could point you to someplace specific. I wouldn't necessarily avoid franchise restaurants; they're certainly a step up from fast food, and they're affordable, but you won't be missing anything if you don't go to one.
I always run into this website when I'm traveling. It has the top suggested things to do in certain locations based on user reviews.
http://www.tripadvis...California.html
http://www.tripadvis...y_New_York.html
(Note that these link to the top "attractions." You can click through the tabs at the top for suggestions on nightlife, shopping, dining, and tours.)