
As some one who's character has an extensive background with the Adventurer's Guilds, I figure I might chime in, even if the general consensus has already been reached. :>
Honestly, I wish more people were into the whole idea of being an actual adventurer. There's an incredibly in-depth amount of lore regarding Eorzea's adventuring workforce, and they're incredibly prominent these days, just as they were prior to the calamity.
Some of the best RP I've had has spawned out of hanging around the guild and grabbing a few guildleves ICly to hammer out with some other adventurers. It's just... ....fun. There's also a ton of lore around guildleves themselves, as they're a huge staple of the adventuring business. Being an "Adventurer" has a lot of background available to it. It was much more prominent back during 1.0, but you literally would go out and do guildleves with your friends as one of the main forms of content for quite some time. Even the first endgame revolved around guildleves. 2.0 sort of downplayed them, but from an in-character perspective, guildleves are a huge staple of the adventuring trade. Echo-induced flashback aside, the original intro did a great job painting the idea of what the adventurer's guilds are like in Eorzea. If you keep an eye out, yes, there are in fact a few civilians hanging around inside, like the two Lalafell that come into the shot at one point.
[youtube]wSZKL1WkGQM[/youtube]
That tangent aside, the Adventurer's Guilds serve three purposes. One, they all happen to be housed in taverns that are open to the public. You most certainly don't have to be registered with the guild in order to have a drink or two. It just so happens that most of the customers are in fact adventurers because the guilds are located inside them. Adventurers come in, have a few drinks, and plan on what guildleves they're going to tackle for the day. That's the primary reason you'd see so many adventurers hanging around, though there are naturally other reasons for adventurers to be there, as well as civilians.
 Two, they have inns, which also are open to the public as far as we know. It's never explicitly stated that they're adventurer-exclusive to my knowledge, and they're quite large. Ul'dah's actually extends out near the gold court, even.
Lastly, they house the guilds themselves, which is what attracts the adventurers. Namely, they house levecounters, which are the only place an adventurer is able to obtain guildleves outside of sanctioned officers of the grand companies who present company-issued leveplates in the field. In order to withdraw guildleves, you are required to be a registered member of the guild, as that specific business is facilitated entirely by the guild in the first place.
TL;DR
The taverns and inns are open to the public, but yes they have a large presence of adventurers for the obvious reason of the guilds being located inside of them.
Honestly, I wish more people were into the whole idea of being an actual adventurer. There's an incredibly in-depth amount of lore regarding Eorzea's adventuring workforce, and they're incredibly prominent these days, just as they were prior to the calamity.
Some of the best RP I've had has spawned out of hanging around the guild and grabbing a few guildleves ICly to hammer out with some other adventurers. It's just... ....fun. There's also a ton of lore around guildleves themselves, as they're a huge staple of the adventuring business. Being an "Adventurer" has a lot of background available to it. It was much more prominent back during 1.0, but you literally would go out and do guildleves with your friends as one of the main forms of content for quite some time. Even the first endgame revolved around guildleves. 2.0 sort of downplayed them, but from an in-character perspective, guildleves are a huge staple of the adventuring trade. Echo-induced flashback aside, the original intro did a great job painting the idea of what the adventurer's guilds are like in Eorzea. If you keep an eye out, yes, there are in fact a few civilians hanging around inside, like the two Lalafell that come into the shot at one point.
[youtube]wSZKL1WkGQM[/youtube]
That tangent aside, the Adventurer's Guilds serve three purposes. One, they all happen to be housed in taverns that are open to the public. You most certainly don't have to be registered with the guild in order to have a drink or two. It just so happens that most of the customers are in fact adventurers because the guilds are located inside them. Adventurers come in, have a few drinks, and plan on what guildleves they're going to tackle for the day. That's the primary reason you'd see so many adventurers hanging around, though there are naturally other reasons for adventurers to be there, as well as civilians.
 Two, they have inns, which also are open to the public as far as we know. It's never explicitly stated that they're adventurer-exclusive to my knowledge, and they're quite large. Ul'dah's actually extends out near the gold court, even.
Lastly, they house the guilds themselves, which is what attracts the adventurers. Namely, they house levecounters, which are the only place an adventurer is able to obtain guildleves outside of sanctioned officers of the grand companies who present company-issued leveplates in the field. In order to withdraw guildleves, you are required to be a registered member of the guild, as that specific business is facilitated entirely by the guild in the first place.
TL;DR
The taverns and inns are open to the public, but yes they have a large presence of adventurers for the obvious reason of the guilds being located inside of them.