Dates would be very helpful in the hunt. I have a Haller in my father's family -- he came to this country from Switzerland, about 1830 or so,
Also, the more you know about where they've lived, the better. I've been doing this sort of thing for more than x50 years and there are few things more frustrating than to hear "he was from . . . (Virginia, Ohio, whatever)"
The 1940 census records are now available, but I don't think they're fully indexed. But the 1930s and back are.