The solution was, of course, a cave. Why? Because this is not Marvel, people. DC heroes do not hang out like commoners in shiny, public (and highly ostentatious) skyscrapers. Dignity forbids. Therefore, like decent people, the Justice League naturally hung out together in a large cavern (like the Batcave, the Fortress of Solitude, the *snicker* Arrowcave, the Aquacave, the Martian Manhunter's mountain getaway, or Barry Allen's absurdly large laboratory in his Central City apartment).
Their "Secret Sanctuary" is presented in their first story (Brave & the Bold #28, where they fight Starro, 'natch) as a fait accompli, no backstory provided. This is the Silver Age, people; information is dispensed to the readers on a need-to-know basis. It was simply a "modernistically outfitted cavern" (circa 1960, that is) that was... somewhere.
So, who do you think got stuck with cutting that chartreuse carpet so it fit flush with the jagged wall of rock on the left? I'm thinking Barry.
You are objecting right now: "But, the Secret Sanctuary was in Happy Harbor, Rhode Island." Well, read the original story more carefully; at no point does it state that the Secret Sanctuary is in Happy Harbor. Starro (or his surrogates--don't ask) attack in three different locations: in the air near an unspecific mountain range, at "Science City", and in Happy Harbor (where that ridiculous dork, Snapper Carr, lives).
In fact, in their second story, where they combat the inept Xotar the Weapons Master, it is specifically stated that the closest town is.... Middledale. We know only that Middledale is somewhere on the East Coast and has mountains nearby (one of which houses the Secret Sanctuary).
Yes, Snapper Carr is seen in the cavern... but after being brought there by Justice Leaguers. Which almost implies that he's NOT nearby. It isn't until the JLA's sixth story ("The Slave Ship of Space!", Justice League of America #3, 1961) that it's shown that Snapper lives close enough to drive to the Sanctuary. Again, another narrative convenience. I contend that the Secret Sanctuary was not originally supposed to be thought of as being in Happy Harbor; you weren't supposed to think of it as being anywhere in particular at all (other than, you know, a cave in a mountain, which is where decent people meet). DC comics are famous for this kind of geographic vagueness; if you want to see an A1 sissy fight, just walk into a roomful of comic book geeks and innocently ask, "So, where in the U.S is Metropolis, any how?"
But the ugly "necessity" of having that babbling moron, Snapper Carr, in nearly every story increasingly pinned the Secret Sanctuary to his hometown of Happy Harbor, which is of course a ludicrous place for it to be. For one thing: it's in Rhode Island, which is pretty much a ludicrous place for anything to be, let alone the headquarters of the most famous superheroes in the DCU. Second, Rhode Island isn't exactly centrally located for either the U.S., hotspots of supervillainous trouble, or the heroes themselves (all of whose cities lie, to some degree, south or west of Rhode Island). Plus, Rhode Island's not easy to get to (unless, like Snapper, you already live there) and its main plus in that respect is that, being on the sea, Aquaman can get there without bumming a ride from Green Lantern or Wonder Woman.
In fact, Happy Harbor is so ludicrously unlikely a spot for the JLA's HQ that almost the only reason to put it there is because...
it's ludicrously unlikely.
Think: if you were a supervillain, would it ever occur to you in a million years that the JLA would hole up in ... a small town in Rhode Island? I mean, unless you noticed they seemed to have a hep-talking adolescent mascot who lives there? And that's really not a criticism of the concept of the Secret Sanctuary being in Happy Harbor, but rather of the concept of Snapper Carr himself. One of many.
Kill it, Barry. Kill it NOW, while you still can.
So in a sense Happy Harbor is the perfect place to put the JLA's Secret Sanctuary, precisely because it's such an unlikely spot for it. As opposed to, say (just off the top of my head)... making Washington DC an even BIGGER terrorist target by putting a "Hall of Justice" on the National Mall, where Batman would have to gas a horde of protestors every time he wanted to land the Batplane. Not that there's anything wrong with that, mind you.
One of the early riddles of the Secret Sanctuary is how the members get in and out without being seen. Sure, most of the members have powers that allow them to arrive fairly stealthily. It ain't called the Invisible Plane for nothing, and, by comic book convention, one can always assume that, given sufficient time to prepare, Batman can do anything, no matter how unlikely, including arrive in the Batplane unnoticed. But the whole theory is spoiled by the same thing that spoils most things in the JLA:
Kill it, Barry. Kill it NOW, while you still can.
Green Arrow, with his idiotic Arrowplane.
blah blah failure blah blah blah Green Arrow blah blah turmoil
There is no friggin' way you can arrive unnoticed in a bright yellow jet fighter... unless you are in the boonies, in a small town whose view of the misty bay over which you approach is obscured by a big mountain. Just like Happy Harbor.
Oh and for those of you still fretting over why GREEN Arrow has a YELLOW plane: stop being stupid, the reasons are obvious.
One: it has to be yellow, otherwise it wouldn't match the Arrowcar.
Be really glad you didn't grow up in Star City.
Two: if you had a sweet jet fighter and wanted to make sure that certified moron and 'test-pilot-whose-job-it-is-to-crash-planes' Hal Jordan kept his stinking green mitts off the darned thing, what color would YOU paint it?