Obviously, no roleplaying in a non-instanced area is ever really private. But more often than not, the illusion of privacy is an important one, and you're possibly aiming for a reasonable level of privacy. It's not that you don't want others to potentially interact with a given scene but that you want to locate your interactions away from bustling areas where you can get lost in the crowd. And heck, there's verisimilitude to consider, since you wouldn't want to have a personal discussion in the middle of a city street.
At the same time, you don't actually want to be completely private because that kills some of the fun of having someone else interrupt the scene. If you go out of your way to make sure no one can ever wander in, you're missing some of the fun that roleplaying can offer.
But there is a time when you'll want to keep things private. No, I'm not talking about ERP and the like; I'm talking about scenes that should realistically be taking place in the privacy of your own home. (All right, that technically does cover ERP as well, but bear with me.) There's a point where semi-private just isn't good enough, and if your game gives you the option, you should take things to a private area.
How do you gauge that? I'm glad I asked. There are five reasons I can think of that combine to make a compelling argument for roleplaying in a private spot, one that's definitely private instead of just off the beaten path.
You're discussing horrible topics. This could be something that's horrible in-game or just horrible in general. I'm not going to judge you if you have a character whose concept involves being abused as a child because that could be interesting, but it's a potential trigger for a lot of people and probably best kept behind closed doors. Similarly, if you're discussing betraying the Federation in Star Trek Online, you should probably not be standing in the center of a UFP space station.
The latter is a bit more of a grey area, however. Sometimes you want your characters to be caught in the midst of doing something inappropriate. It all comes down to what your goals are for your character and his or her interactions; are you trying to keep a secret or do you want to be outed?
You'd be absolutely mortified if someone saw you. The aforementioned Sad Sith Dance falls under this header. We all do things in private that we would never do in public, whether that thing happens to be singing, dancing, or acting out the cutscenes from Mass Effect 3 while impersonating the voice actors. If your character would be ashamed to do something in public, odds are good you shouldn't make that happen.
This doesn't mean you shouldn't always keep something potentially embarrassing private, however. A shouted argument in a semi-private area can draw attention, and attention might be exactly what you want from the scene. It might even be better to gauge what would embarrass you as a player rather than your character.
You need to maintain scene continuity. There are certain times when roleplaying is following a pretty tight script, when you need things to feel dangerous or isolated or singular. If you have a group of players stalking a dangerous killer only for said killer to turn the tables, it kills the mood to have someone wander in partway through. When the scene can't handle interlopers, it really needs to be away from interlopers.
Sometimes, this is also the case when you really need everyone to agree on a certain conceit, but not always. If you need to make it clear that there's a cage in the center of the room, you might be better off in a private area just so that no one wanders through the cage and then asks what's going on. Then again, many people will maintain a respectful distance from the entire scene until they know what the heck they're looking at, so it's not always mandatory.
You're personally apprehensive. There are some characters that are hard to get right the first few times you play them. It's helpful if you're not under the pressure of performing for a potential audience for those early tries, especially since you might toss your character's personality and demeanor through a few revisions before you go for the gold.
You're involved in ERP. Because honestly.
As always, feedback is welcome in the comments below or via mail to firstname.lastname@example.org. No, I will not post the lyrics to the Sad Sith Song. Next week, I'm going to answer an excellent question by a reader last week and set down a basic definition: What the heck is roleplaying and what are you doing with it?
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.