It is difficult to say that any Japanese Generals were "highly regarded" in the public imagination of the Allied countries; the most commonly known people were Tojo and Hirohito. What was known of them was mostly caricature, done for propaganda purposes. Japanese Army generals did not engage American forces until near the end of the war - it is almost helpful to think of the Japanese Army and Navy as fighting two totally separate wars during this period.

Probably the answer to your question then is the Japanese Navy Admiral Yamamoto. This man was one of the major players in developing the Japanese Navy's air and carrier capabilities. At his heart he was a "Big Battle" thinker (influenced by an American theorist named Mahan) and out of this thinking he planned both the Pearl Harbour raid and the opening phases of the Battle of Midway. He was considered so dangerous and important that he was effectively assassinated; ambushed while over Bouginville by a flight of American P-38 Lightning fighter planes especially sent to shoot him down. This mission was authorised personally by FDR, reportedly with the words "Get Yamamoto", and was codenamed Operation Vengeance (just to stress to you how symbolically important killing this man was seen to be).

The best General from the Army and probably the one most famous to military historians in the west (even if no-one else cares), is General Tomoyuki Yamashita, "the Tiger of Malaya". This man captured French Indo-China and forced a surrender of British-held Singapore (for a total of 120,000 soldiers). His own command numbered 30,000. This was probably the high-point of his career: he was politically unappealling, and the first excuse was used to reassign him to a backwater.

Near the end of the war, he was placed in charge of the Philippines with roughly 250,000 soldiers, with which he attempted a Fabian-style retreat into the mountains. Unfortunately, Admiral Sanji Iwabuchi objected strongly to the plan and unilaterally re-occupied the capital city of the Philippines (Manila) with 16,000 Japanese sailors. Against Yamashita's clear orders, he then attempted to clear the city of opposition, which resulted in conservatively at least 100,000 civilian deaths.

Yamashita has a mixed legacy. His war trial was so contentious, that it actually set a new precedent called "Command Responsibility", or the "Yamashita Standard". Essentially, the trial decided to hold Yamashita responsible for his soldiers' behaviour despite clear evidence that the three main defence points were proven: that he issued orders to the contrary attempting to prevent the behaviour; that he didn't know and wasn't told about some massacres being committed within his command; and that some of the crimes with which he was being charged occurred outside his chain of command. Quoting Defence Attony Henry Clarke:

"The Accused is not charged with having done something or having failed to do something, but solely with having been something....American jurisprudence recognizes no such principle so far as its own military personnel are concerned....No one would even suggest that the Commanding General of an American occupational force becomes a criminal every time an American soldier violates the law....one man is not held to answer for the crime of another."

The trial, however, established that a commander is always responsible for his area of command, that therefore Yamashita was responsible. He was therefore found guilty of war crimes, sentenced, and executed. The precedent the decision established still endures today; that an Officer is accountable before the law for crimes by soldiers even if they did not order them, attempted to stop them, didn't know about them, or had any means to stop them.

EDIT: =/ I am not a spelling master-mind.

Though not a very well-known figure from the Pacific War, General Tadamichi Kuribayashi was seen as a very smart strategist and cunning leader of his troops in the Battle of Iwo Jima. Despite the fact that almost the entirety of his 22,000-strong force of soldiers were killed in the battle, his troops managed to kill almost 7,000 Americans, and wound over 19,000, making Iwo one of the few battles in the Pacific War where overall casualties on the American side were larger than the Japanese. He did this through the use of tunnels and caves honeycombed across the island, brilliant firing discipline (holding fire until the exact moment when Japanese machine-gunners could inflict maximum casualties), and the discouragement of banzai charges. In Derrick Wright's The Battle for Iwo Jima, he describes the respect that Marine Corps General Holland "Howling Mad" Smith had for Kuribayashi. As the fighting on Iwo began to pick up, Smith, after studying battle reports, reportedly said

"I don't know who he is, but the Japanese General running this show is one smart bastard."

Also, after the battle was over, according to Wright, he tried to identify Kuribayashi's body so he could pay his respects and give the General a proper burial, but was unable to do so since it could not be found. Lastly, in Smith's own autobiography, titled Coral and Brass, he tips his hat Kuribayashi, stating

"Of all our adversaries in the Pacific, Kuribayashi was the most redoubtable."

While this didn't make Kuribayashi a hugely famous war figure (like Yamamoto) who many people could name off the top of their head today, it definitely does make him one of the few Japanese generals who was given recognized by his American counterpart in battle, General Holland Smith, as a shrewd strategist and worthy adversary, thus gaining his respect. One place you might recognize his name from is the Clint Eastwood film Letters From Iwo Jima, in which he is portrayed by Ken Watanabe.