Why did the British choose to attack the United States at the site of New Orleans?

Because, The New Orleans was the gateway to the interior of the western frontier.

Explanation:

Just to add a tad bit on the answer, it can be added that the British attack to New Orleans took place in the context of the War of 1812. Great Britain and the United States had just committed to end the war, but a few days later, on January 8, 1815, the two nations and their respective armies resumed fighting. The British deemed the port of New Orleans to be a key location in their plan to invade the territory in the West that had just been purchased by the United States. They, nevertheless, did not succeed in taking the city.