It would heavily depend on who you consider "most important", also it depends if you include the several Nazis who were tried in absentia. These are generally who would be considered the most "important" Nazis captured.

Martin Borman, one of those tried in absentia, was head of the Party Chancellery after Rudolf Hess flew to Britain, and of the closest confidants of Adolf Hitler

Rudolf Hess, was basically the same as Borman, but had fallen out of favour after he flew to Britain to offer peace terms.

Karl Donitz, was Hitler's successor and led the Flensburg government that succeeded Hitler's Nazi Germany.

Herman Goering was Hitler's designated succsessor for most of the war, was head of the Luftwaffe, and one of the architects behind the final solution.

Joachim Von Ribbentrop, head of the foreign affairs ministry, and played a role in Nazis decision making and the final solution

Wilhelm Keitel, was extremely loyal to Hitler, head of the OKW (supreme Army Command) and issued a number of orders to kill POWs.

Finally, Albert Speer. The close personal friend of Hitler, who was armament minister who authorized the use of slave labour.

See the issue with trying to figure out who is "most important". This isn't anywhere close to everyone who was tried at Nuremberg. If we are going by rank, Karl Donitz was the highest ranking Nazi who was captured. If by importance to the Nazi movement, Borman and Goering were both instrumental to the development of the Nazis and did the most "damage" in terms of atrocities, but thats hard to categorize.

I would disagree that "most of the important Nazi leaders" did not face trial, the majority of those who held important positions were indicted and tried at Nuremberg.

Hitler, Himmler and Goebbels may have escaped through suicide, but you still had Goering (effective no.2 until 1945), Keitel and Jodl as important political figures from the army, several figures involved at high levels within the SS, two important figures involved with the economy and forced labour.

In fact, the majority of the indictees at Nuremberg were "important" if this means they held relatively high status within organisations/bureaucracies and enough evidence to at least indict them on the four charges.

Adolf Eichmann is among the biggest fish that have been actually tried in person I guess. While not super high in the Nazi hierarchy in theory (Lieutnant-Colonel), he was responsible for the whole logistic of the final solution and was therefore one of the most directly involved in the matter.

The way Nazi hierarchy worked was one of competition between underlings and politician struggles between the higher ups. It meant that in practice the higher you went, the less they would actually dirty their hands directly so they could blame any failure on someone else more easily or just feign not knowing anything about the matter to save their heads.

Concretely, it meant Hitler probably said something along the line of "The jews are an issue, we have to get rid of them completly" to several of his underlings. Then these underlings would interpret Hitler's order and then order someone between them to actually carry the matter in a way they thought would be pleasing to the Fuhrer.

Adolf Eichmann was basically one of such men. Göring had ordered Heydrich who ordered Eichmann to do it.

Göring would therefore be higher up but the real person who actually organized all that in practice was Eichmann (after Heydrich is killed by Czech resistance).