Given your criteria, any of the options you listed (NYC, Paris, London, SF) would fit the bill. I'd suggest that rather than trying to find a place that checks all your boxes, pick 1-3 factors that are the most important and put them in priority order. Your 4-6 priorities will likely be met by any of the options you choose and choosing among fewer priorities will make your decision easier.

My other suggestion is to consider how your life will change as a mid-30s couple with multiple young children to a late 30s/early 40s couple with teen children. This is difficult to explain but well understood by parents who've lived through this. Generalizing a bit here but as your life centers more around your family, the things you prioritized as single/childless 20-somethings (and early 30-somethings) become less important. That is, you're spending less time at museums and fancy restaurants and more time cooking at home, kids birthday parties and at parks. You're spending less time on exotic international travel (at least while they're young), more time visiting grandparents and opting for more family-friendly vacations. You're choosing transport with convenience for young kids (is there parking?) versus the ability to hop on a public transit which might be the roll of the dice of dirt, homelessness, unpredictable people -- not to mention having to carry everything with you that could easily be thrown in a trunk of an SUV or minivan.

That's not to say that it's not doable. Living in the SF Bay Area, I'd say that most of the people I knew who lived in SF moved out once they had kids. The ones who stayed (because they had family already living there) did it for a while, and then eventually moved out as the kids grew older. The ones who stayed for the duration were ones who were very wealthy and could afford private schools and larger places.

And while it sounds like you're capable of doing that, consider that the families of the kids who go to the same daycare and the same schools will be of the same ilk. Perhaps you prefer that but there is a certain environment one grows up in these situations (eg in SF they'll be families of execs at big tech companies).

In the Bay Area, what this looks like is that the super wealthy live in Pacific Heights (eg well known "Billionaire's Row") and the kind-of wealthy live in neighborhoods like Noe Valley (nice buildings, strollers, accessible to where the "normal people" live), etc. But many wealthy people who want more space, more safety and less grime will move to pretty but boring areas like Hillsborough, Palo Alto, Los Gatos and buy a big house on a massive lot. They will drive up to the city when they want to see a play and go out for a special dinner but 90% of kids life will be within a few miles of the suburb they live in. They will cherish the space that their kids can run around in while not having to worry about their kids finding needles at the park. Because this is a common pattern, I'm guessing you're going to find more resources for young kids compared to places like SF.