That must have been a different story... or you are remembering wrong.

The..... Hexcave?

Yeah, what a Prankster.

Or, Hex's bordello, known as "The Hex Hut".

In the original cave headquarters of the JLA?

--wyld

Good guesses all-- but nobody's right yet.

The crashed remains of the JLA satelite headquarters ?

That, or the JSA's place.

Titan's Tower?

Titan's Cave ?
Titan's Bar & Grill ?
Titan's Attic ?

One of Lex Luthor's hidden lairs (I think it was underground/in the sewers if I recall correctly)

Correctamundo!

Bonus question:

I don't know the answer to this, and can't find the answer online. What is the name of Hal Jordan's surviving brother, and his kids? Probably not the right spot for this, but if I can't even figure it out with full use of the internet, it might give you pause.

Unless I am mistaken, both brothers are alive. Jack (is single) and Jim (married to sue, don' know the kids' names.

Here's a little something to help you out:

Hal Jordan's known Relatives:

Martin "Marty" Harold Jordan (father, deceased);
Jessica Elizabeth Jordan (mother, deceased);
Jack Jordan (older brother);
James "Jim" Jordan (younger brother);
Sue Williams Jordan (sister-in-law, married to Jim Jordan);
Jason Jordan (nephew, son of Jack);
Jennifer and Jan (nieces);
Howard Jordan (nephew, son of Jim, god-son);
Jane Jordan (niece, daughter of Jim),
Jeremiah Jordan (uncle);
Lawrence "Airwave" Jordan (cousin);
Helen Jordan (aunt, wife of Lawrence);
Harold Lawrence "Airwave II/Maser" Jordan (cousin, son of Lawrence);
Doug "Hip" Jordan (cousin);
Titus Thomas Jordan (uncle);
Steven Jordan (nephew of Titus Jordan);
Grant Emerson (created with Hal Jordan and other JLAer's DNA);
Yellow Lantern (Bizarro duplicate);
Hal Jordan (Draal clone);
Pol Manning/Doctor Strangehate (power ring created replica, 5707 AD);
Lizzie Jordan (descendent in far future)