No, most airlines don't have a relationship with gas or grocery stations in most areas. The couple that might only do so in a tiny portion of the US, so without mentioning where exactly in the US you will be and which airlines you're interested in collecting (just AA or also others?) it's hard to help you more on that.

(In the US, the deals on gas/groceries is that some points-earning cards, such as the Hilton HHonors Amex, give more points for certain caegories like gas and groceries than for other non-hotel purchases. So unlike Canada, you have to have a specific credit card to be able to earn points at most gas stations and grocery stores. Some grocery chains have their own points programs, but they just earn cash back or maybe discounts on one brand of gas, not airline or hotel points. But they're independent of your payment method, and thus "stack" withi it; ie, you can earn those store-specific points while also earning whatever you earn on your card.)

Will you have an MC or Visa card of any sort (credit or debit, and Canadian is ok)? If so, you can register for the dining program of, say, AA (AAdvantage Dining). Then, if/when you dine at participating restaurants, you earn miles on those dines, even if the card you're using doesn't earn miles itself.

And unlike online shopping sites (which check addresses against cards, and thus may not let you make a US-delivered purchase with a Canadian card), the dining program doesn't care what your address is, just your card number. (It will ask you for your address, but it doesn't check that against the card, it only uses that for marketing purposes. In fact, due to a bug with the dining programs' website, Canadians can only register for the dining program by giving a "fake" US street address!)

Go visit the FT iDine/Rewards Network forum for more on the dining programs.