It's fitting that the Free League doesn't have an actual building for a headquarters, for that'd rather defeat the purpose of "freedom." Throughout Sigil, a number of places offer safe haven to lndeps - usually in exchange for their hiring on as guards for some future caravan run.
The Free League considers all visitors to the Great Bazaar — the Indep headquarters — as potential customers, which means everyone gets treated more or less the same. So long as bashers don't tease the twoheaded pigs in the livestock pavilion or blow their noses in the silk cart, they're free to shop as long as they like. A basher in need of jink might check the Debtor's Pole. Merchants from all over Sigil use the pole to post the names of sods who haven't paid their bills. Some names have rewards attached. A basher who returns a wanted sod to the creditor named on the pole pockets the reward.
Unlike most other faction headquarters, the Great Bazaar isn't contained in a single building. Rather, it's spread out over a magnificent open-air plaza, a huge square of tents, shops, and stalls. The Bazaar is a cacophony of sounds — shouts, clanks, shrieks, barks, whistles — and a sea of smells — hot bread, peach perfume, fresh paint. Though generally confined to the plaza, the Bazaar has no formal borders; a merchant who can't find room to set up shop on the plaza is squeezed onto a side street. On any given day, then, the Great Bazaar might not only be Sigil's busiest faction headquarters, but also the largest.
But the Bazaar does offer one thing of genuine value: freedom. The lndeps see to that. A merchant's free to ply his trade and get an honest wage for it; he doesn't need to gild the hand of some high-up like he might in one of the other wards. Even the smallest peddler can take his wares to the Bazaar, and the lndeps make sure he gets booth space that won't cost him his firstborn. The Bazaar changes constantly, never the same mix of sellers from one week to the next - part of the reason it's taken so long for the lndeps to realize their ranks are vanishing. But the taverns, inns, stables, cafes, and other permanent establishments that line the plaza provide a network of safe houses for the Free League. One of them's the Red Lion Inn.