I'm not sure of any stories involving Americans hiding Japanese necessarily, but there were several modestly sized organizations, primarily made up of elite, well educated, whites - who were against internment. These groups were based in San Francisco, Berkeley, and Los Angeles. They would do things like send school supplies, newspapers, and other modest donations to the camps. Some representatives from these groups were also able to visit the camps. They returned back to the big cities and spoke to audiences about the abuses in civil rights, detention, and things like lack of medical care.

Others, like photographers Ansel Adams and Doretha Lange took photographs documenting the experience of Japanese Americans during the war.

Edit: I should mention some larger, national organizations were also opposed to internment. For example, the American Civil Liberties Union (ACLU).

Even among opponents, the perception of internment was different from the perception of the shoah (please excuse my vocab choice, my spelling is atrocious). While the shoah was billed as a way to get rid of the "Jewsih problem," interment was a way to keep an eye on the minority until the war was over. It was an injustice, but not an extermination, and a main problem was simply that they were being forced out of their homes to somewhere supposedly humane but unpleasant. If you hid them, they'd still be exiled from their homes and kept somewhere unpleasant, plus the authorities might assume they were traitors and seize their property. This perception appears to have even been held among the Japanese Americans, as I have yet to find an account of physical resistance or flight.