If Germany had the Atomic bomb and some of the other advanced weaponry as you suggest, I think the Germans would have started by using a jet bomber to attack Moscow. The logistic would be difficult (and essentially a suicide mission), but the speed and surprise of such an attack would have decapitated much of the Soviet Union's command and control infrastructure, and even its logistical infrastructure (many of the rail lines deliberately passed through Moscow, a legacy of the Tsarist Empire and a means of control by being able to dispatch troops and supplies from the Imperial Capital), effectively stranding much of the Red Army and blunting their ability to continue offensive operations against the Nazis in Eastern Europe.
Attacking London would be much more problematic. While it would be easier to send a jet or even a conventional fast bomber, the Germans actually had a certain amount of "respect" for the British, and Nazi "mythology" was receptive to the idea of an Anglo-German partnership in the New Order. (Like a lot of other ideas floating around in the Nazi universe, this wasn't well defined or spelled out in a lot of detail). The Nazis also knew that "decapitating" the British Empire was not going to work at one stroke the way it might against Soviet Russia. Churchill himself spelled it out in a speech ("We will fight on the beaches"):
We shall defend our island whatever the cost may be; we shall fight on beaches, landing grounds, in fields, in streets and on the hills. We shall never surrender and even if, which I do not for the moment believe, this island or a large part of it were subjugated and starving, then our empire beyond the seas, armed and guarded by the British Fleet, will carry on the struggle until in God's good time the New World with all its power and might, sets forth to the liberation and rescue of the Old.
Bombing the UK would bring about redoubled efforts from the nations of the Empire (Canada alone had more than a million men under arms by this point, and the world's 3rd largest navy, despite being a very thinly populated nation at the time), and even with the resources of all of continental Europe under the command of the Nazi empire, they still would have been badly outmatched by the resources of the British Empire alone, much less America and the rest of the Allies as well. This does not even take into account that most of the British Empire was well beyond the reach of any conceivable Nazi war machines being built or contemplated in 1944; how would the Germans be able to stop the raising of armies and industrial plants in Australia, India and South Africa, for example?
The other point that should be noted is there were lots of notional "allies" like Brazil and Mexico, which were supporting the Allies and nominally part of the alliance for diplomatic and economic reasons. The unleashing of atomic weapons on European targets by the Nazi regime might well have been a tipping point for some or all of these nations to change from notional to "real" allies. There would have been a lot of pressure from the senior partners like the Americans to contribute (having these nations as allies up to this point was more to keep them and their resources away from the Axis), and the example of nuclear attacks could also have convinced them that the Nazis were not just a theoretical evil or threat, but a clear and present danger. (Alternatively, this could also have been enough for many nations to renounce their membership in the Alliance and become Neutral, with lots of second and third order effects. One can Imagine the Americans invading and occupying nations which could provide a springboard for Nazi shipping and aircraft, for example).
This would be a fascinating contra factual to explore in more depth. We have not even looked at how Imperial Japan or Fascist Italy would have looked on Germany newly armed with atomic weapons, for example.