So one of the lesser-known stories of the Cold War is that wherever the US nuked, they became very interested in. So Hiroshima and Nagasaki got extensively studied, as an obvious example. And the reason is pretty obvious as well: the US was interested in knowing as much about nuclear weapons effects as possible, so they could anticipate what an attack on them, or an attack on others, would look like in the future.
So one of the fields that really, uh, boomed as a result of US nuclear testing was the study of coral reefs and atolls, because those were what the US was destroying when it set off nuclear weapons at the Pacific Proving Ground (i.e. the Marshall Islands, Bikini, Enewetok). The US government funded a lot of research into the ecology of atolls, the effects of radiation on underwater life, and other fields. So it is one of those areas that we know a lot about as a result of Cold War science, even though the connection to weapons is a sideways one.
As for "anything interesting" — well, it depends on how you define "interesting." No kaiju, for better or worse.
But the study of nuclear weapon effects, especially in relation to ecosystems and atmospheric science, is directly related to later understanding of climate change. The historian Paul Edwards has written on the overlap there. So I would call that an "interesting" result of studying nuclear weapons effects via testing and other means.
The scientific spin-offs from the nuclear side of the Cold War are much wider than most people realize, because nuclear war was such a concern that it led to a lot of funding for anything even marginally related. One example I like to give of this is that one of the major funders of the Human Genome Project was the Department of Energy, who isn't who you might think would be a top sponsor. But the DOE, like the Atomic Energy Commission before it, was long one of the major funders into genetics research, because it was concerned, ultimately, about the effect of radiation on our long-term genetic legacy, because of a Cold War fear about a post-apocalyptic environment. So there is a definite connection there, from the bomb to our knowledge of our genes.
France tested a few of their nuclear weapons in the Saharan desert within Algeria prior to testing them out in the pacific. The Saharan tests ran in the 60s, the first of which called 'Gerboise Bleue'. Testing of the weapons actually led to a great deal of protest within the area and worldwide, led by the Saharan Protest Team.
As far as what has been found in the area since, I am not too sure. Being that it is the Saharan Desert, I can't imagine much would be left, but I do remember finding some pictures which had manakins and fake buildings around the test area. Not sure if they are still there today.
Depending on your definition of 'interesting', you might be interested in trinitite, formed from the first nuclear test in New Mexico.
The Nevada Test Site was used for The US testing. The best way to find out about it is to take the tour. The craters are pretty interesting but no Godzilla to be seen. Mostly it's just craters in a gigantic desert kind of cool from a moonscape perspective.
Well in Australia there was a test site used in the 50's called Woomera which in the local aboriginal language means 'spear thrower' which I haven't been able to find out conclusively if it predates weapon testing or was called that because of it. As for anything interesting being there and discovered there isn't much historically but anecdotally there has been issues around chronic illness in people and live stock.
A fun little tidbit about french testing in the pacific. The bikini islands got hit with quite a few bombs, one of them required the local population to be moved before the test and a cordon enforced. As a result of this while the crater reef and island is still very dangerous for human life the reef and marine life is actually healthier than it's surrounds and functions as a eco-refuge as humans aren't allowed in the area so they are free from fishing and other influences.
Edit: forgot to mention it was for the Brits as Australia does not have nuclear weaponry and later Woomera was a location for a immigration detention centre in the 00's as rainbowplethora mentioned and flash point for protests around Australian dentention policies.
There was a Documentary yesterday about the early years of atom bomb testing in the Us and th USSR. Unfortunately It is in only available in Frencch or German:
http://www.arte.tv/guide/de/050144-000/die-atombombe-im-vorgarten?autoplay=1
There are incidents discribed like the case of Walter Greg, whose home was accidentally hit by a bomb in 1958, because the pilot accidentally hit the trigger. Fortunately the bomb did not detonate.
A big thing apparently in the early years were so called 'peaceful detonations' where they just blew huge craters to create lakes or even planned to bomb a new canal to substitute the Panama Canal.
I don't have the background to answer the part about whether anything has been found in the area or not. But this YouTube video is related and interesting. A time lapse of all detonations by country since 1945. http://m.youtube.com/watch?v=_W_lLhBt8Vg