I'm not sure there's any one thing. When I think of New York City, which I would say is not only vibrant but nearly vibrating with energy, it's some combination of the following:

* A ton of different languages being spoken within earshot at any one time

* Lots of different smells at any one time, some delicious and certainly some much less so

* Lots of music where you do and do not expect it, all sorts of different genres sometimes complementing and sometimes juxtaposing the surroundings

* People physically moving and speaking faster

* The physical tightness of the city probably adds to all of the above

But most importantly, I think the above compose into an overall sense of serendipity. The phrase, "in the city, anything is possible" is frequently interpreted to mean, "you can achieve the highest version of what you want to achieve!" I think that's actually incorrect. It means exactly what it says: anything is possible. Relative to suburban or rural areas, you simply have no idea what is coming next minute-to-minute. That, I think, gives a sensation of constantly anticipating serendipity, which we round out to the word "vibrant."

> "in the city, anything is possible"

I am reminded of this and grateful anytime I get interested in a new hobby. I started indoor rock climbing and discovered there are at least six gyms in my city that I can bike to. I got interested in film photography and found there was a great community darkroom with all the equipment needed to develop film and make prints. I discovered I enjoy board games and found there are dozens of clubs that meet regularly that I can choose from, depending on what types of games I like and how competitive I want the atmosphere to be. (Asterisk on all of this currently, due to the pandemic of course.)

This is a good description of the city intangibles.

I think it usually boils down to stuff like this.

Coffee shops, bars/pubs, cinemas, theaters, opera houses, bigger and nicer libraries, real, physical bookshops (at least for people like me, who visit them regularly like how other people are going to church), and I’m sure I must be missing some other stuff.

As an anecdote, I went through a dark time about 10 years ago and living in a big city and being able to see strangers each and every day on public transport helped me tremendously, it meant not having to live with my dark thoughts. I could have not had the same experience had I lived in suburbia or in the countryside.

My own hot take on this:

If the fundamental unit of value is provided by people, then the potential to get work done scales with the number of people engaged and ready to do it.

In a city like New York, there are a lot of talented people that are engaged in value creation. That creates an economic ecosystem that provides the potential to take an idea and bring it to value delivery with low friction.

Vibrancy, then, is the attribute where idea potential is able to reach value delivery with low friction.

This is evidenced by a lot of what the other posters have mentioned: restaurants, the arts, startups, etc. These are the result of that potential existing within the ecosystem.

It's hard to say. I've lived din large cities in Europe almost my entire life and that experience was "normal" then moved to the US suburbs where almost nothing happens. But a few years later when I visited New York and stayed for 3 nights, oh man, it was such a weird energy. It felt like I needed to be out every second, it felt that if I spent an hour sleeping in my hotel it's an hour wasted somehow. The fact that at any point in the day or night there were people filling the sidewalks made me want to be out there with them. I don't know how to explain it, but there was an energy driving me to do more.

I don't think it's easy to describe in words. You actually have to be there. I've lived in a suburb of Toronto for most of my life (similar to a random American suburb), and when I went to Florence for the first time, I had a sense that the city was alive, independent of the people in it. It felt as if I was a part of something, even though I was just visiting for a couple of weeks. On the other hand, I didn't feel that in Rome.

I can offer contrast between where I grew up, Cleveland, which is not a vibrant city, and Los Angeles, where I live now.

In Cleveland, no one walks. It's jarring when I visit home now and sometimes not seeing a soul walking beyond the occasional drunk down on their luck, even downtown. Even the poorest people here save for a $1000 car, and they can manage it because rent is $400 and insurance is dirt cheap. As a result of all this non walking, most restaurants and shops are located in suburban style developments with hundreds of cars parked in the lot. These are extremely popular. The Eaton Chagrin shopping center, for instance, gets so much traffic the exit ramp backs up onto 271 for a mile and the parking lot typically fills up entirely. I've never seen traffic quite like this in LA, spilling out from a highway offramp directly into a shopping center and gridlocking an entire interchange. Things are slow during rush hour in LA, but traffic actually moves, you are never stopped for 10 mins not moving at all unless there has been a serious car accident.

As a result of all this nonwalking, the few commercial corridors that were built in the streetcar era perennially suffer. For lease signs are more common than open signs, but luckily these rare small lot commercial parcels don't get turned over for development into big box agglomerations very often since the population of the metro area has been entirely stagnant for 50 years. This means that every restaurant and every bar is a drive, and this is a drive you have to make yourself as sometimes it takes 20-30 minutes to wait for an Uber to make it's way to your neighborhood, given the low demand and low density of the population. This is a recipe for a neutered nightlife, neutered pedestrian life, and serves to further amplify the feedback loop of clearing more woods in the fringe suburbs for tract housing and developing more suburban shopping centers.

Because of white flight, the city never really recovered. Cleveland used to have 1 million people living in its borders, now it's 380k, and the city is remarkably hollowed out and many historical buildings have been razed for surface parking. Urban development has focused on getting people downtown for a sports game and nothing more. The bars downtown are a recent phenomenom, brought on by millenials being drinking age and having literally no bars beyond suburban family taverns, bowling alleys, and formerlly smokey dive bars to frequent.

Then the winter hits, and things truly die. No public events really happen, and people just stay in their homes and try not to spend much time in the cold. If they want to spend time in the cold, they drive 4+ hours to upstate New York where there are ski resorts that take longer than 30 seconds to go down the hill.

In LA, every single street has someone walking. Every major artery has a bus that comes at least every 10 mins during rush hour, and I made extensive use of the busses before the pandemic. In other words, because of this sprawling high frequency bus network, the streetcar feel of the city never went away. Commercial corridors are sustained if they are on a bus line with decent ridership. My bus stop was even able to sustain a man who would be there every day in a canopy tent, selling solely roasted peanuts and socks (I'd like to think he started with a wider selection then ended up refining his inventory to his best selling commodities). Also on that corner was a cell phone repair store that also sold excellent crepes, my barbershop, a fruit seller, several weekend vendors, two taco trucks, a pizza shop and night club, several filipino restaurants, four markets, and in the evenings a churro vendor. And this is a rather unremarkable corner in the Rampart Village at first glance, but teeming with vibrancy for the pedestrian.

I walk down a random residential street in LA, and I have good odds of encountering someone selling elote, or sliced fruit, or a truck selling whole fruit directly out the back. The city feels like it's teeming with life, teeming with entrepreneurs, teeming with small business. Before the pandemic, it was rare to see a vacant storefront. Even now, local businesses are doing a lot better than I anticipated and few are folding, versus Cleveland where it seemed like in any given commercial corridor that wasn't a brand new strip mall, vacancy might be 80%.

In short, a vibrant city is like a vibrant ocean reef. Teeming with all walks of life everywhere you look.

A formerly poor neighborhood in the process of being gentrified.

Hilariously enough my artist friends are moving to the racist white trash neighborhoods because those are the only places where they can afford the rent. Here's hoping an art school drop out doesn't get ideas in such an environment.