My family was mainly from Walls/Sandness, with the Jameson name setling down around 1750 as far as I can tell.
Although one or two relatives on other branches definitely went to the U.S., the only ones I know anything about went in the late 1800s. Most of the known emigrants in our bunch ended up in the U.K. - especially the ports (especially Leith and Liverpool) or in Australia and NZ, all in the late 1800s or early 1900s. However, some people probably went to Leith in the 1700s and their descendents may well have ended up in America.
When did your family go to the US?