As most of the other answers said, it's simply Amazing! I will give you some reasons from my experience.

The city that never sleeps: like they say, for a city that never sleeps, a lot can happen in one night! It is does never sleep. I've stayed out till 3 am bar hopping with friends and then went to a diner at 4 am, still as busy as it can be. I have actually had food delivered at 2am using seamless, the food delivery app. The city transit does not stop at all, and in some parts of the city it stays crowded. Plenty of 24 hours gyms and people will actually go there at very early or very late hours.

Restaurants: they say including bars, there are some 40,000 places in NYC that you could eat at! So basically you could eat each meal at a new place every time if you wanted to. The price range varies but some places, the quality May surprised you. I love how in each neighborhood there is that small pop up place or tiny eatery where you get the best certain recipe. weekend brunches are big among New Yorkers and some places can have very long waits on Saturday/Sunday brunch times. Needless to say, you can get food from any part of the world.

Summers: Summers are best in NYC! Some days can be very humid but for the most part they're great. A lot of companies actually let their employees work an hour or so extra daily but take Friday's off so for some, every weekend is a long summer weekend. Central Park is so beautiful in summer, everyone is out in the park or on the street. There is a certain energy in the air and everyone is just in a happy place. On weekends, a lot of the people head to the beaches around the city to come back with a nice tan. If you want to go out of Manhattan but not too far, head to Brooklyn for a different sort of eccentric young crowd and good street food.

Rooftops are the best in the city, there are so many of them with amazing view but they can be very very crowded.

Winters: a lot of people worry about the winters in NYC but trust me, it's nothing like winters anywhere else on the NE. You may be very few people on the street but walk into a bar and you feel as if winter never happened. My friends would have “hurricane party” whenever there was a storm warning which would basically be a sleep over with a lot of tv/movies and board games. The transit system runs most of the time during snow even unless it's really really bad.

Daily life: well I was doing my residency there so I was very busy but typically, if I got off work early, I would go for a run or bike ride in the park, some days the gym. Then either eat in or go out for dinner with someone. Dinner was always followed by a walk and getting a dessert, either from one of the local bake shops or if nothing else, a brownie from Starbucks. Weekends were always busier than weekdays! Wake up, do laundry if you want to feel productive, go out for brunch with friends which would last for hours, with half the group buzzed from the bottomless mimosas, followed by a movie, more walking and dinner, followed by crashing at whose ever place was the closest.

The bad parts: there were a few things that I would like to mention:

• it took a while to establish a good circle of friends. My theory is that the locals know that most people are in transit so it takes them a while to let you into your circle if you're new to the city. But you will always find people who are new like you and very open to connect.
• Rents truly are high, that applies to San Francisco as well I understand but I mean, I have seen studios for 3500–4000 in luxury buildings, which totally sounds crazy but at the same time, you can find a studio for 1300–1600 in neighborhoods like Harlem or Inwood.
• Dating can be hard. There are so many options in NYC that ghosting is very common. People will just disappear on you. You do it to others and others do it to you. It's almost understood and most people have experienced it so much that they don't make an issue out of it. Then there are the tourists who are in the city for a few weeks but want to have a serious relationship with you… I mean, come on!
• Traffic! Forget your car if you're moving to Manhattan. It's not just the expensive street parking and long term parking but it actually takes a lot longer to drive within Manhattan than to take the train.

Comparison with San Francisco: I have not lived in San Francisco, I visited for a week so my opinion is probably not valid. But here are a few things I noticed.

• Uphill downhill is fun until you get tired of walking uphill again and again. I walk a lot in NYC. Half a mile to the train every morning, another half from the train to work. But in SF, going uphill was just a pain!
• Homeless people, don't get me wrong, I feel for them but just for the sake of comparison, there are many in NYC but SF was a bit too many.
• Still had to cab or drive to some places with in the city. Everyone knows how extensive NYC subway system is.

Yes NYC is expensive, crowded and dirty, but there's a reason no one wants to leave the city. I call it the curse of NYC, people will complains but then would never want to move out. I would definitely recommend living there to anyone be it for a few years, just for the experiences that you can get from living there.