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The "crime free" thing is hard to pin down and is a matter of perspective.
You could live in a city that has high crime stats, but depending on your neighborhood you may never know it. Similarly, you could live in a high crime neighborhood of a low crime city and have the opposite perspective.
My recommendation to the OP would be Nashville. Maybe Cincinnati as a sleeper.
"Four seasons" in most of the United States can be quite different from any of the populated areas of Australia. With the exceptions of Hawaii, coastal California and much of Florida, there can be periodic extreme cold weather events in winter, sometimes with paralyzing ice and snow storms. Having a large continental landmass at higher latitudes makes for a much more rigorous climate than what exists in the Southern Hemisphere.
Just a key point to be aware of especially as many of the recommendations are for American cities with a lot to offer, but with sometimes serious winter weather as part of the package.
I almost never recommend NYC here when a somewhat vague question like "where should I move next??" comes up, not because it's not a great city (it is, obviously) but because living here is typically a series of compromises and the financial burden shouldn't be underestimated. That said, since you asked to evaluate based on your criteria and only your criteria, then I think it's a solid recommendation. I've separated the first question from the others, with the first being a "yes, but":
1: As crime free as a city can be: Stats will show that NYC is one of the safest big cities in the US. The obvious qualifier here is that coming from Australia, nearly every city will have more crime than what you're used to. But relatively speaking, NYC is safe.
2: All four seasons - yes, 4 distinct season with warm, humid summers, cold winters with occasional snow, short springs and glorious autumns
3: Lots of restaurants, cafes and bars - yes
4: A big nightlife and music scene - yes
5: A large variety of shops to choose from - yes
Since you didn't mention it, I'd assume you have a big enough budget to swing it. I'd probably focus on Brooklyn as it's probably the most fun & lively area, though that may be my personal bias coming through.
Other cities that may qualify would be Chicago, Boston, Philly, DC, Atlanta, and Nashville. These are kinda the usual suspects that get thrown out there. But if you're not budget or career constrained, just skip the smaller cities and jump straight into NYC as it has everything that you'd want, and on a massive scale.
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