The Yasukuni-jinja shinto shrine is interesting from several points of view. To start with, the buildings and surrounding grounds are pretty interesting, especially since the entrance gate is massive - the largest "torii" or shinto temple gate in Japan.
Also interesting are the politics of the place, because this shrine is strongly associated with Japanese right-wingers, who are strongly nationalistic and want the Emperor to be Prime Minister (ie, they want the Emperor to be Emperor). The Yasukuni-jinja website (which is in English and Japanese) contains some material which nicely illustrates this sort of extreme view. I've copied an article from the website called "A Correct View of History", just in case it gets removed from the museum's website in the future. The shrine is dedicated to the two and a half million Japanese who have died in war, and it's disturbingly inclusive - here lie the ashes of Prime Minister Tojo, who many believe masterminded Japan's entrance into World War Two, and who was hanged after the war as a war criminal.
Not totally coincidentally, the shrine is very near the Imperial Palace in Tokyo, though the shrine is very old and predates Japanese World War Two nationalism by a long period. Visits to the shrine by Japanese prime ministers and other politicians are still very controversial. All in all, it's a totally different experience from the Hiroshima Atomic Bomb Peace Museum.
However, for me the main reason for visiting wasn't the shrine itself, but the Yushukan war museum which is part of the shrine complex. Not much Japanese military hardware survived the war (a situation which is generally true for countries defeated in war), but there are some interesting pieces of equipment here, including the first locomotive to traverse the Thai to Burma railway, made famous in the film Bridge on the River Kwai. There's also a World War Two Suisei ("comet") dive bomber which was rescued from the island of Yap and restored, and a tank recovered from a Pacific island battlefield.
One of the most interesting features of this museum is the prominence given to euphemistically named "special attack operations" - in other words, kamikaze suicide attacks. The theme starts outside, with a statue of a young airman which I later found out was labelled "kami kaze", and several rooms inside which are devoted to displays of individuals and the weapons and circumstances under which they carried out their "special attacks". There are two especially significant and authentic pieces of equipment in the museum which were of the types used in these attacks. The first is a kamikaze mini-submarine, really a converted torpedo, which ironically is on loan from the American Navy! There's another example of these submarines at the USS Bowfin submarine museum at Pearl Harbor. The other one is an "ohka" ("cherry blossom") rocket powered kamikaze plane which was to be carried underneath a bomber until near its target and then piloted at high speed into an enemy ship. The rocket technology for this particular aircraft was used by the Germans on the Me163 Komett rocket-powered fighter, and later sold to the Japanese. Again, there are examples of the ohka in America, with a very good one on display at the Marine Air-Land Museum at Quantico, Virginia.