This is the CoolCar and its vehicular bretheren's educational equivalent. It's often an AcademyOfAdventure and/or an ElaborateUniversityHigh, and frequently an ExtranormalInstitute, but none of those tropes apply in all cases.

So then how do you know it's this trope? The Cool School is too cool to be your school, a school that's probably very good at teaching, thanks to no shortage of funding and/or a Reasonable Authority Figure (or a few). Expect the textbooks and the Applied Phlebotinum to be full of Dangerous Forbidden Techniques and Sufficiently Advanced Technology or Magic respectively if the setting is in any way fantastical. If it isn't, it's probably one of the weirder school types not in the Extranormal Institute list like the School Of Seduction or Clown School and/or has a Wacky Homeroom if it's not a Wacky College. The Library will be at least well-stocked, and there's a chance it's a Great Big Library Of Everything.

Despite this, it's not always sunshine and roses. The villain(s) will attack the school if there are any, the Rival School will almost certainly be full of spoiled rotten over-privileged Jerks With Hearts Of Jerk that put the Cool School's resident Jerk Jock and Alpha Bitch to shame (in the other way), and the homework is often brutal.

The Cool School is often a Boarding School but never an awful one (unless the villains have made a hostile takeover), and the protagonist will lament either often or on rare occasion about how much life at home sucks and they're much happier at the Cool School.

The Trope is often a Wish Fulfillment fantasy of the writer and almost always one of the fandom. Who wouldn't want to go to/have gone to this school? Even if it's dangerous, it's never the kind of place that treats you like National Student Database Entry #78956723567606 or just the $1,000,000,000,000 "donation" for a new school building, and what you learn there is going to be useful.

This is where you will find the Stranger In A Strange School, any schools which really are ordinary Boarding Schools but are in a City Of Adventure, the normal Muggle public school that somehow manages to do its job well, and is the trope where you should list anything that doesn't fit under the normal examples of overlapping tropes but is definitely too awesome to be real.

The ExtranormalInstitute[=s=], including those that teach something other than AcademyOfEvil holding the VillainBall, AllGhoulsSchool being a professional emo, HeroAcademy saving a damsel, NinjaSchool being a sneaky zen master Franchise/StarWars who is one with the LifeEnergy, RoyalSchool running a fantasy empire ConspicuousConsumption when a tutor would do just as good a job, SpySchool defeating the bad guy with the VolcanoLair on IslandBase an island in the middle of the Pacific Ocean VideoGame/EvilGenius or is in the process of building one, SuperheroSchool defeating the other supervillains everywhere else as well (Franchise/XMen or hiding from racists acting rashly BewareTheSuperman out of fear), and of course WizardingSchool magic will fall into this trope unless they're the kind to CrapsackWorld avoid like the plague.

Examples of Cool School include:

Advertising

Anime and Manga

Comic Books

Fan Works

Film

Literature

Live-Action Television

Music

Myths and Legends

Newspaper Comics

Oral Tradition

Pinball

Podcasts

Professional Wrestling

Puppet Shows

Radio

Tabletop Games

Theater

Video Games

Western Animation

Web Animation

Web Comics

Web Video

Other Media

Real Life