<PERSON> syndrome blocking ICBMs
Start with a more extreme version of the space race. Say instead of stopping at V-2 rockets, Germany launches a V-3 rocket, the first ICBM (with a conventional payload) late during the war, impacting somewhere in Brooklyn. Although completely inefficient as a bombing strategy, this leads to a general panic in the US public (and in Russian leadership after the war, when you combine this rocket with the atomic bomb) and even more advanced German technology for both sides to use after the war.
As a result, Sputnik goes up in 1952 and the US soon follow. In the next decade, both sides launch stuff into low earth orbit like there is no tomorrow. Satellites, capsules, small space stations with telescopes to spy on the enemy (hand operated, as the electronics are still at 1950s level), spent upper stages, maybe even a few nukes, just to have them at hand. Just add up all the proposals the military made during the space race and finance them.
However around 1960, everything goes haywire. Maybe there is some high speed collision of two unmarked spy satellites, maybe some anti-satellite weapon is tested, maybe a rocket launch fails spectacularly while nearly in orbit. 898
No matter what, now you have a lot of high speed debris, which in turn starts to hit other things, which then also tend to explode, astronauts and cosmonauts jump into emergency capsules back to earth, leaving their stations unattended. In short, the utter chaos of a <PERSON> syndrome erupts, the lower earth orbit fills with trash. Both sides blame each other, but there is nothing that can be done except to wait for a few decades while stuff slowly deorbits.
With this, ICBMs suddenly become useless, as most of them will not survive the flight. Both sides of course start to invest heavily in fast bombers and shorter range atmospheric missiles, but of course equally in the methods to intercept them. As a result, the destruction is not so assured anymore. Some stuff will get through, coastal cities like New York and St. Petersburg might easy enough to reach, but anything heading towards Moscow or Chicago will be spotted and shot down.
As added benefit of this scenario, the resulting high amount of shooting stars will make night scenes so much more romantic... 500