The following map was created by Andy Kierz at the website Business Insider. Much of its content is not surprising: the most common jobs for immigrants on west coast are in agriculture, in the south housekeeping and construction. But note that in four states — Maine, Michigan, Missouri, and Ohio — the most common job held by immigrants is college professor.
I notice, too, that in a number of Southern states with histories of anti-Labor legislation, the most common occupation is “construction workers.” In Ohio, “right to work” seems temporarily on hold, but the legislature is focusing instead on undercutting prevailing-wage rules.