I love Cynosure (obligatory Grimjack shoutout), and I've read a few other takes on the City that Lies at the Heart of the Dimensions, but I'd adore seeing a bunch of locations that could fit in -- the more culture mash-up-y the better!
Let's start with the obvious: Hell's Kitchen. A neighborhood co-extensive with a section of one of the rings of Hell. Originally home to violent gangs and planar peep-show houses. Eventually gentrified, and now known for it's restaurants showcasing Hannibal Lecter-esque haute cuisine.
01: The vast aquarium where the exotic fish tak on the faces of those who have passed by.
02: The market stall where a blind woman and her deaf husband sell powdered emotions. A pinch of hate costs a pittance, but a few specks of the grief of falling from Heaven as your feathers burn around you is pretty much priceless.
The Kross-Time-and-Space Go Organization (KiTS-GO) is a organization dedicated to competitive playing the ancient (Chinese, Kara-tur, Rokugan, whatever it is in that dimension) board game Go. Because of the organization, official rules have stayed consistent in at least 427 dimensions for over 894 years. Despite players often leaving for years at a time, and some unable to even appear in person, a systematic ranking has been in effect, with Drillbald Veng, a sentient gelatinous cube (don't ask) having taken the top spot for the past 38 years. Denab Bonitz, a baruer fighter, is the current carekeeper of the club proper, a converted bowling alley below street level below the Erzatz Elemental Evokers in Exile foreign legion post #10732 on the corner of Smith St. and Hexaxenoquodopolu Ave. Game nights are held 3 times weekly, and new players are encouraged to play (no entry fee, but expect to be repeatedly asked if you want to become a member). Just be respectful, no open flames (see E. E. E. E. 10732, above), and mind your crumbs if you bring snacks (they tend to attract mice, which spontaneously develope sentience in Drillbald's presence, and they are terrible at Go). Adventurers can stop in to lose, recruit new party members (a surprising number of high level barbarians are formidable Go players), or gain (often highly esoteric) information.
Ernst's Battery Exchange. Interworld travellers soon discover that there are no cosmic standards for power cells, which makes recharging your gadgets a problem if you're not an electrician. Fortunately, Herr Ernst—a chubby middle-aged German from the first half of somewhere's 20th century—is. He has a small staff and a large, well-swept, electrically-lit warehouse with attached workshop and manufacturing unit. The shelves are piled with boxes of dead cells, spare parts, bottles of acid, bars of metal, etc. He keeps common types of battery in stock in the walk-in areas of the warehouse (pick what you need, check out at the front) but the usual method is to drop off a sample cell. They'll analyze it to bits, then make you a set of acceptable copies within a couple of days. Ernst also does generators, motors, adapters, convertors, and cables—if it involves electricity, he'll take a crack at it. Antimatter costs extra (safety), but he's got the cheapest nanocoils in the city. He once made successful mundane substitutes for a Taranian magic lightning crystal, though the crown it belonged in came out several kilograms too heavy to wear on one's head. You get a substantial discount if you bring in detailed documentation in a language and mathematical system he can interpret.
Business has been so good, he has contemplated expanding into cartridge ammunition—trade your 5.56mm bullets for another world's 5,55's, that sort of thing—but is concerned about the morality and mortality of entering the arms trade.
Not far from Ernst's you will find one of the city's (number variable by time of day) outlets of its biggest translation service. Depending on where and when you're going it can provide mystical knowledge of the required languages, comprehension viruses, limited-use telepathic comms, and even language lessons if you're going really far from the centre. They can also refer you to gear, technology, costuming, and if necessary body-sleeving facilities before a trip off-reality. They used to rent tourbots as well, but you know what happened there.
A vast network of catacombs under the city has become home to numerous creatures that dislike or can't handle sunlight. Over the years it evolved to a clubbing neighborhood for alternative subcultures. Here they come to dance with vampires, mosh with orcs and drink with trolls. Many crypts have been converted into Goth(ish) clubs, Metal(ish) or Punk(ish) bars. The bones that were their original occupants turned into decorations and drinking cups. Which might not have been the best idea, some restless spirits take offense.
A public park, noted for a variety of hanging and standing lanterns, some of which light themselves. There's a Japanese-style half-moon bridge over a small stream, a lot of rocks and greenery, and a large wrought-iron gazebo. The park is a common hang out for jazz musicians, who favor the acoustics of the little river valley in combination with its position below some public walkways. There's a concert every couple of nights.
Realities sufficiently out there that visiting endangers physical or mental health. The Transdimensional Police keep a watchful eye on the borders, and only the bravest or craziest try to sneak in to steal something from The Land Of Perpetual Wednesday.
There are rumours that certain popular cartoons are actually filmed live in a Quarantine Reality, but I sure don't want to go and check...
A certain place outside the usual city-limits - surrounded by an enormous wall made from an unknown, apparently-indistructable material inscribed with ancient magical wards - intersects with the beginning of a universe. Hidden beneath the enormous, heavily-shielded complex of machinery and magecraft on one side of the wall is a hole, thinner than a human hair; enough energy escapes from that hole to power the entire city, with room to spare.