Tokyo is full of baffling attractions. Even more mind-bending is that most of them actually make perfect sense when you stop to think about it. Part of the fun of visiting Tokyo is tuning into the city’s unique sense of “normal”, so consider some of these unusual must-sees and get into a Tokyo frame of mind.

A cup of coffee and a feline friend
Some cat cafes are just coffee shops with a handful of preening cats, others are full-blown feline palaces with baskets and cat trees instead of tables and chairs. At Cat Café Nekorobi, visitors shed their shoes at the door and get down on their knees to pet and play with the well-groomed animals, paying by the hour for the privilege.

While it sounds odd at first, if you take into account that most Tokyo apartments do not allow pets (and those that do cost a premium), cat cafes start to make sense. They function as a sort of public pet centre – in the way that parks make up for an absence of backyards.

Anime maids in real life
A cafe in Tokyo is also more than just a pit stop; it is often a place where reality is suspended and where Tokyoites can get a brief respite from the accumulated stresses that come from living in one of the world’s biggest cities. Maid cafes are a perfect example. Here, the servers dress as maids, with frilly white aprons over waist-cinching black dresses, and greet customers with a deferential “welcome home master” (or mistress). But this is not some fantasy pulled from thin air: the image of the maid has been popularised in many manga (Japanese comics) and anime (Japanese animations) series. Maid cafes like @Home Café in the Akihabara district offer fans a chance to enter this world -- and leave theirs behind -- if only for an afternoon.

Family-friendly communal bathing
You can tell a lot about a culture by its leisure activities, and in Japan, getting naked with total strangers -- the custom of visiting an onsen (natural hot spring) -- is a perfectly normal, family-friendly pastime. The Japanese love bathing so much that in Tokyo there is even a theme park devoted solely to the act of soaking: Oedo Onsen Monogatari. There is no thrill-seeking here, just relaxation. Visitors spend the whole day going from tub to tub, breaking only to stroll through a re-creation of feudal-era Tokyo, also on the premises, while wearing a yukata (light cotton kimono).

Food that looks real enough to eat
Food is also high on the list of Japanese obsessions. Turn on Japanese television any time of day and at least half of the shows will be about food. Japanese cuisine lends itself well to the screen because so much emphasis is put on presentation. This also goes a long way towards explaining the plastic food models displayed in front of restaurants --  no description of a dish is nearly as appetising as a visual representation of it. Kappabashi-dōri is the district in Tokyo where commercial restaurant supplies, including plastic food models, are sold. Not sure why this should count as a Tokyo must-see? Check out the level of detail and craftsmanship.

Really expensive, rarefied edibles
The department store is another place to gawk at perfectly crafted food – real food, this time. The city’s basement store food halls, called depachika, are home to the infamous $100 melons and other such rarefied edibles that Tokyoites purchase as gifts. It is not just the taste and texture that warrant the hefty price tag, though. Note the perfectly even grain of the skin and the straight stalk that prove this melon was handled with care (and gloved hands). Tokyoites do not do their everyday shopping here; the fancy fruits are meant to be gifts. And In a city of small apartments and precious shelf space, there is no better gift than a perishable one.

Umbrellas from a vending machine
When it comes to personal consumption, far more Tokyoites get their food and drink from conbini (convenience stores) and vending machines. Both offer an excellent peek into the daily rhythms of the city’s commuters and can be found on every street corner. Japan has more vending machines per capita than any other country. In addition to hot canned coffee and bottles of cold green tea, vending machines have been known to dispense such necessities as canned bread, beer, umbrellas and hot noodles. They are also increasingly high-tech: some have touch screen menus and face recognition software to track and respond to the preferences of identifiable demographics.

Washroom washlets
But no Japanese innovation inspires more awe than the washlet. These are the electric toilets equipped with water spraying nozzles that clean your nether regions at the push of a button. The more sophisticated ones also have seat warmers, air dryers and water pressure adjusters. Some even raise and lower the toilet seat for you. Flushing toilets were a wonderful invention, but why stop there? The development of the washlet is a perfect example of kaizen, the practice of continuous innovation and improvement.

An 18m-tall, 35-tonne robot warrior
The city’s largest paean to technology can currently be found on the bay in Odaiba. Here stands a one to one scale model of Gundam, the giant “mobile suit” from the epic anime series of the same name. The statue was originally created for a two-month run in 2009 to mark the 30th anniversary of the series, but thanks to intense popular demand, it is back for another year-long run until spring 2013. With any luck, this 18m-tall, 35-tonne robot warrior will become a permanent fixture. It would not be a bad emblem for a city as ambitious and seemingly otherworldly as Tokyo.

The article 'Tokyo’s strangest sights' was published in partnership with Lonely Planet.