Upvote:4
Perhaps you are not familiar with the US West? Even today (and more so in the 1940s & 50s) there are places where you can be miles and miles (substitute km if desired) away from anything much other than sagebrush and rattlesnakes. The tests were conducted in such locations. (Note that Las Vegas wasn't much of a place in those days, either.)
OTOH, those "remote islands" were mostly populated. When later H-bomb tests were conducted there, the military had to remove the populations from them, in addition to the logistical problems of transporting the bombs, monitoring equipment, and support staff. See e.g. Bikini Atoll.