As I get older (into my 30s) the less I feel like using youthful slang, and I take extra pride in using professional English. But I can't think of a word that is universally equivalent to the colloquial term "cool" that means "worthy to judgmental youths" or something of that nature.
Could you suggest some more professional-sounding terms that can be used instead? Something that would be appropriate to put in a book or research paper or news report on the topic of "coolness".
I agree that the term, cool, is inappropriate for a formal letter, research paper or even a magazine review if the audience is known to be experts themselves in the subject. To say a film is cool is reductive and might get a few of your readers rolling their eyes. Ironically, I believe that to be cool one ought to avoid using that expression; it's becoming overused, but that's my personal opinion.
The OP ought to consider how people from the 40s, 50s, 60s and possibly early 70s would have expressed the same concept. (Now someone will tell me that "cool" meaning impressive, admirable, inimitable, and wow was first used in 1800s or thereabouts.) 1
When I was living in London as a child, cool usually meant mildly cold or indifferent, wicked was associated with witches and criminals, and sick meant vomit. We did use bad though, when we meant "very good".
However, much depends on who your readers are. If I had to describe a new car or a hi-tech gadget, and compliment it on its design or features I might very well opt for "a cool design" and "cool features". But if I wanted to be more specific, (or original) I'd choose from one of these adjectives instead: (in no order of preference)
For a film/movie review you would probably need a different list, unless you were commenting on the camera shots then many of those suggested above would fit. A "cool" movie could also be described as being:
Actually, I'm beginning to realize just how versatile "cool" is...
If you searched Google for "cool meaning", you will find a substantial list of definitions. According to your given context above, an appropriate definition would be under (3) (informal):
fashionably attractive or impressive
"youngsters are turning to smoking because they think it makes them appear cool"
synonyms: fashionable, stylish, chic, up to the minute; sophisticated, cosmopolitan, elegant; le dernier cri; informal trendy, funky, with it, hip, in, big, happening, now, groovy, sharp, swinging; informal kicky, tony, fly; black English: down "she thinks she's so cool"
With all that said, I would like to suggest "socially popular", as it should fit well in your example sentences. (Though personally, I think there is nothing wrong with the use of the word "cool" in those places.)
Depending on context, you can try:
neat, tidy, spruce, polished, dapper, immaculate
shiny, lucent, glace, lustrous, sheeny, dazzling, sparkling, fulgent, effulgent, ceraceous, resplendent, refulgent, brilliant, patinous, agleam, radiant
waxy
slick, velvety, smooth, satin, satiny
spiffy, dandy, natty, swank, chic, classy, arty, dashing, smart, stylish, snazzy, pizzazz, jazzy, grandiose, elegant, recherche, frilly, baroque, deluxe, ritzy, lush, ornate, majestic, palatial, sumptuous, exquisite
splendid
opulent, rich
delicate
fragrant, ambrosial
heavenly
graceful, lambent
blazing, flaming
In terms of labelling a human, simply popular is your best alternate. It's that simple.
Note however that (as I think you suggest) "cool" (when labelling a human) can have three main meanings:
Cool as in Joe Walsh
Cool as in sang froid (although this is less used by young people, only boring old people use it this way)
Cool as in simply "popular", "popular with young people". ie essentially a label for the currently popular pop or film personality. (Err - or youtube, or whatever.)
Your best alternative for the first is relaxed, for the second icy or smooth, and for the third popular.
Note too that there are more "slang" (so to speak!) uses of it: I think the most prominent fourth use is "He's OK," i.e., "He's not with the cops; you don't have to be suspicious of him; even though he's an adult you can trust him not to be a dickhead" and so on.
Finally note too that, as you probably know, "cool" is wildly out of date for anyone under .. what .. 60, say? I feel it's very unlikely teenagers (2015) would say it today, at all.
