To your questions about its popularity, yes and no...
The service and food is not that great, but the room rates are fairly cheap and there are a few "regulars" who are willing to provide other "services" for the sailors who put into port in Argentum for a single night. So yes it is popular to some degree for that reason.
No, there are other inns in the nearby area (Screaming Raven and Swaggering Sailor are a couple of the others in the Light Tower District (that have been detailed so far)), although the density of such places is a little lower than in other parts of the Channel Cities relative to the population density of this district.
Yes, it is also a "no questions asked" type of place, and as such is the hangout for a portion of the Channel Cities underworld NPC's as well as various nefarious plots and activities.
Unfortunately I don't have much in the way of details up on the Channel Cities wiki yet (progress on that has been extremely slow in recent years), but here is a link to the map of the
Light Tower District (district F2 on the
Channel Cities grid map).
Hoping to find time to add more details to the wiki as well as to write more articles covering locations and places of interest within this setting in the future, but unfortunately spare time to work on such things tends to be very limited. But feel free to ask any other questions and I'll do my best to answer them. On that note however, I had written a series of "story" articles of sorts in some of the early Guild Companion issues (back when we first launched, started in the December issue of 1998) covering a little bit of details of the Channel Cities written as a story between a newcomer to the Channel Cities with a couple of locals residents. The first one can be read here:
http://www.guildcompanion.com/scrolls/1998/dec/world_of_aernth.html They provide a little bit of background that might be of interest to anyone who may find the setting interesting.