I would think the most important thing is ability to find a job in the new city.
The websites I would check are sites like best places to live in the US or US healthiest cities, that sort of thing. There are also lists like top ten friendliest cities, if you like friendliness, and I usually look up crime rates also. Crime rates you can plug in your zip code and the new zipcode and compare. I think it’s good to compare, because you know how you feel in your current city, but might be very unaware of the actual crime rates.
There are several different online calculators where you put in a salary for the city you live in now and the calculator tells you how much you need to earn to be even in the new city. The calculators aren’t perfect of course, but it gives you an idea.
Financial things I would really pay attention to are taxes, everything from sales tax to income tax. Some states have property tax on cars, which for my husband and me is a big increase in expense. When we lived in TN the sales tax was 9.25%! If you are big spenders that’s a lot of money. They taxed groceries in that state also, which a lot of states don’t.
Check out realtor.com and look at the housing. Beware that it still is very important to actually see the areas. You might see a very attractive new house that looks great online, but it might be being built in an area of town that is just starting to go through a rejuvenation. That can be fine, but it depends if you are willing to take the risks associated with that.
I’ve lived in many different places, my best advice is visit before you move go there and shop in the supermarkets, check out whatever makes your daily routine pleasant for you. Available gyms, libraries, parks, clubs, whatever it is. Feeling settled for me has a lot to do with the house/apartment I live in, convenience, climate, access to a pool, and feeling safe. I have another friend who feels settled once she joins a tennis club and starts playing and making friends there.
I also like being near a hub airport so I can fly nonstop easily. That might not matter to you.
Arts scene is often good near universities, or places with lots of Jews. Although, when I lived in Memphis the local theatre was excellent. That was a surprise to me.
Here in the Tampa Bay Area the arts are fantastic. We have the Dali Museum in St. Petersburg, the collection is incredible and there is always an additional exhibit of a featured artist. There is another art museum in that city that is lovely. The symphony here is wonderful, three large performing arts theatres within an hour of each each other, Broadway tours, all sorts of historical cities nearby. Lakeland, FL has FL southern college designed by Frank Lloyd Wright, the Morse museum in Winter Park has an incredible collection of Tiffany that it literally takes my breath away. I doubt Tampa Bay really meets all your criteria, but my point is a lot of times cities and regions of the country have things you don’t expect.
Lastly, you can always move again if it doesn’t work out.