Since the 80s, Japan has been seen as very 'futuristic' in the west. Some combo of extreme density and a high percent of the economy being manufacturing makes people more comfortable with technology, and that's reflected in their pop art and music, on top of the normal exoticism of a non-western language and culture.
Aside from this, their (extra future-y) nerd culture is more accessible to westerners through manga, anime, and video games than countries like China or India.
They also have fewer taboos about mixing sex and digital entertainment, so things like dating sims and porn games probably draw a segment of the particularly digitally comfortable into Japanese culture.
That means it can just seem incredibly cool and fun, while it's actually a relatively boring country in the scheme of things
The answer to why geeks love Japan is probably going to vary by geek. Japanese culture is broad and full of deep practice. It offers many obsessive exports, any one of which could fully consume someone with the geek mindset, from ikebana and origami to J-RPGs and painting Gundam figurines. It only takes one of those hooks to grab a Westerner and steer his/her interest toward the rest of Japan. Anime is just one possibility on a long list.
It's worth keeping in mind that Japan was ascendant during the formative years of many of the geeks here. We all rode to school in Japanese cars, played games on Japanese consoles, took pictures with Japanese cameras, studied Japanese in school so we could be future masters of the universe, and so on. Many geeks on the academic fast-track got a lot of exposure to Japan from a young age, and it still holds our interest.
Japan is a modern country with a modern economy, so I'd bet you'll find a lot of folks on these tech forums who've lived and/or worked there. I worked over there myself.
Finally, interest in Japan is not limited to Westerners. Some of my best friends when I lived in Tokyo were from places like Ghana, Bangladesh, Brazil, etc. Everyone is intrigued by that weird country, not just white people.
Many are going to say something like "Japan is a hyper-modern country set against ancient traditions, which is so neat" or "Japan is historically X so Y happened after Z and therefore we've been interested since year NNNN". That's all fine and probably indirectly, abstractly correct. But I don't think it captures the more visceral and immediate reasons that so many geeks personally take interest.
All the more special is that it's also the nr 1 non-western economy, i.e. not the US or Canada or Australia or Europe, which will feel familiar to anyone living in those countries. Even irrespective of it being an economic powerhouse, it feels culturally more differentiated from the west, than say South-America is from North-America, or Eastern-Europe is from Western-Europe.
Combine that with a long history of civilisation, and you've got THE major (economic) superpower with its own distinct culture. There's no such story in the rest of Asia, Africa or South America. All other countries are either economically struggling, or are culturally/historically insignificant, or are simply too small like Singapore.
I don't think we even have to fully explore the interesting relationship Japan has with technology as part of its post-war economic and cultural story and many other such facets like it, to answer the question. None of the interest in Japan feels at all illogical to me.
To a kid growing up in this time, Robotech (with its long-form structure, complex characters, and real death of major, beloved characters) was fucking Game of Thrones.
This same generation would grow up with Nintendo and Sega, and all the Japanese-originated games on those platforms. So it's not surprising that as young adults we would becone attached to the culture which produced all this stuff.
This allowed them to do stories and themes that western animations could not touch, because they where expected to be broadcast for kids.
Perhaps the best example could be Legend of the Galactic Heroes.
https://en.wikipedia.org/wiki/Legend_of_the_Galactic_Heroes
You are looking at 110 episodes, each 25 minutes long, covering what is effectively a naval war in the stars. But with it you have intrigues of all stripes, and no real good guys.
[1] https://en.wikipedia.org/wiki/Diegesis#Film_sound_and_music
[2] http://kotaku.com/5990702/why-you-havent-seen-any-new-macros...
Another show that got such a treatment is known as Saber Rider and the Star Sheriffs in the west. The original name was Star Musketeer Bismark.
That said, the rework allows us to experience Peter Cullen (Optimus Prime) putting on a cowboy drawl.
i am not into anime or other such things but have recently picked up my first manga: all you need is kill, solanin, and pink. but i would say i am interested in other cultures just as much. it typically revolves around design though. haha. and i a not even a designer in occupation.
this might of interest - a post by me about Muji:
http://jugad2.blogspot.in/2010/05/muji-simplicity-is-decepti...
Source: initially I got hooked on Japanese music (then anime and the rest followed)
Part of the appeal of Japan is that it has a very visible cultural export market (anime/manga/video games), and that is driven in part by the fact that Japan is a very populous country: it's the second largest "rich" country (loosely defined here as OECD sans Turkey and Mexico).
Japan's history also helps in this regard. Its relative isolation kept its history from being the more-or-less samey nature that, say, European history. The samurai, while being almost a carbon copy of the western knight, is just different enough (the vastly different roots helps obfuscate the similarities) that you can pretend that samurais aren't knights, and it's not hard to make media that focuses on them in this light. This makes it easy to sell Japanese history as "cool."
I think the main factor is economics: post-war Japan was well placed to export its culture. Around the 70s/80s Japan, in being the most economically developed of the East Asian countries, was trading the most with the West. At the time, China was still on lock down for example, and Korea's growth curve was later and smaller than Japan's.
This period coincided with TVs becoming more common in the household, and later came VHS and consoles, and Japan was able to cement a position of exotic appeal in pop/alt culture as access to and variety of media increased.
In the mainstream you had things like Karate Kid, Ninja Turtles and Mario. Slightly less mainstream you had things like DBZ, Sailor Moon and Akira.
It probably also helps that Japan feels more "familiar" to the west: Japan has democracy and homosexuality is not illegal, for example. I would hazard that factors like this make Japanese culture somewhat less foreign to follow than say Chinese culture which may be smeared by anti-communist sentiment.
On my end, what fascinates me with Japan is how they developed in relative isolation for such a long time. My ultimate dream would be to explore and learn about alien cultures and languages; in the meantime, I feel that the closest I can get to that is Japan.
Maybe also a bit due to interest in Zen, is my guess. E.g. See ESR writings, etc.