To get nuclear weapons used, you'd have to alter American foreign policy thought right back to 1946. Nuclear bombs were initially thought of by military planners (most notorious among them Macarthur, who wanted to use them as tactical weapons to support his invasion of Japan if that nation didn't capitulate, and later in Korea) as really big explosives. However, as the 1940s wore on and American politicians applied pressure to shrink the standing army, the Americans began to use the nuclear bomb as their Last Resort, a boogeyman weapon that would be invoked if the Soviets tried anything. Of course, this left the US in the position where it was unwilling to use the atomic bomb when Stalin expanded his sphere of influence into minor eastern European nations.
So, find a way to get a moderate conflict between American and Soviet forces (not necessarily the US and USSR going to war, but rather a proxy war, perhaps in China) at some part of the world around 1947-8. Get a small atomic weapon used in combat, as a tactical weapon, and you've cemented the atomic bomb in military planning as a tactical device. From then on, the precedent for using it in a purely battlefield environment is set.
Of course, this could evaporate when MAD sets in at the time that hydrogen bombs and worldwide delivery systems become practical.
So, either Korea or China are your best bets. Get the US involved in beating Mao's forces, get American boots on the ground, drop a 30-kiloton device on the Communists. The results of this? Perhaps China is split between a north and south China. Perhaps the Soviets feel free to use their own tactical devices in Afghanistan (should that occur) or perhaps both sides have no concern with selling 'small' (circa 10 kiloton yield) devices to their proxies.