D-Day Failed, the War Lasted Longer, More than 2 Nukes (But Not Fallout)
The success of the Normandy landings and allied invasion of Nazi-controlled Europe heavily relied on deception and secrecy. Would would have happened if the Nazi's (such as Rommel) saw through the deceptions of Operation Bodyguard, perhaps because the Enigma code was never broken and the Nazi secret agents in Britain weren't captured? Or if a very highly placed spy evaded detection and could smuggle out the secret?
Uh oh. There is no guarantee that Nazi Germany actually wins with this small change, but it virtually guarantees the war doesn't end swiftly. It's important that the Allies not get wiped out completely, but significant losses and a forced retreat would delay invasion for many months at least - or years.
What happens during that time? Well, it's very possible that the A-Bomb is figured out by more than just the US. You could say this forced a stale-mate, perhaps after much of Europe was liberated (or not), or that the Nazi's still lost but they managed a number of controlled nuclear explosions. If some of these nukes somehow had made it to the US, this may have tremendously changed American sentiment towards war. Suddenly war, and technology itself, seems all like a Pyrrhic Victory. Everything is terrible, what's the point of anything?
This doesn't need to be a post-apocalyptic wasteland or anything, but more than enough to really inflict the horror on everyone world wide in a way that doesn't happen when only your enemies are effected by it and it's "your" invention. Perhaps there are enough nukes for Germany to not completely lose control but give up most of it's holdings (bonus if Hitler is killed in a nuclear explosion and his less extreme generals regain control and drive the Nazis to be less insane). Extra bonus if we end up with a worn down and wounded US, isolated former-Nazi Germany in Europe (still in shambles and all teeth removed), USSR with similar destruction and no allies won from the end of the war, and your choice how Japan goes. Maybe they still lose, maybe the allies are forced to a similar concession and Imperial Japan remains.
The result is no comparatively easy peace. No people remain enthusiastic about the war or the glory of technology, and a worldwide depression may have set in as trade remains isolated and international cooperation remains limited and fragmented into many mutually bitter groups.
In this environment it's very possible that everyone becomes increasing isolationist. There's no real reason to develop international jet liners, and the post-war largesse of the US government (and good ole American Taxpayer) is not available to fund the sciences while Europe rebuilds. No Big Bad Undefeated Buggy Monster exists - everyone is hurt and pulling away from the world scene. No one is enthusiastic for anything that seems even vaguely connected to the horrors they've seen from war, and this sentiment extends to Universities and science as a whole in the view of the public. In this world, "the good old days" really were better back then, before all this supposed "progress" tore things apart. Hard to argue with when a famous city in your country can't be visited anymore because it's an irradiated wasteland.
Then what? Well, whatever you want to happen in your story! If science, technology, central government authority, and capitalism vs communism doesn't play out in 1940-1960, the world would surely be a very, very different place!
And the cost? Probably better German codes (better Enigma), or a few well placed spies that screw up a single military operation - and a lot of guessing what happens next.