This is an important question for an artist even if they don't ask it of themselves. First of all I don't think you have an audience for your work in the way the question suggests. At any given time your audience changes, as your work changes and as your exposure changes and as your venues change. At any given time an artist may have multiple audiences. It also seems reasonable to say that if your work is seen anywhere, you have an audience whether you consider them or not. If you do consider your audience, your consideration may be a dangerous thing for your work if you decide who your audience is and try to court them.
I have shows most commonly in two types of venues, non-profit spaces which are mostly University and College spaces and commercial spaces. Though considerably less of the second one in recent years. My most typical location for an exhibition these days is a University gallery.
The typical audience for this type of show is an art student. Of course non-art students go to these shows as do faculty who are both connected to art and others who are not. When I think about this audience I have several ideas that I want to express including showing them something challenging but also I want them to think about painting and how painting is applied and pictorial space etc.. Basically all the things that I want my students to look at during a painting class. When I show at a University, I am still thinking about teaching and I am also thinking about the show from the standpoint of a visual concept.
The second type of venue that I most commonly show in is the commercial gallery setting. This is a different experience and different from time to time and from gallery to gallery. These shows can be "safer" because the work needs to sell and possibly have a broader appeal. The gallery director usually has a broad say in what goes in and where it goes etc. These shows can feel a little more controlled.
They can also be very exciting as the viewers are usually art consumers, they are typically dressed nice and the crowds can be large. Of course these are generalizations but more often than not, this has been my experience. The audience for these shows will be a mix of people who are knowledgeable about art from a theory/history point of view and those who are just into art.
I sold the above painting at Perry Nicole Fine Art Gallery (now closed) in Memphis TN. The painting had already been sold before the opening and at the opening the couple who bought the painting came. The lady asked me what their names were and I said the title of the painting is "Two Cows Traveling." She said "no, what are the cows names?" It had never occurred to me that someone would think about these as literal individuals but she was.
When I was first exposed to this question, I had two voices in my ear. One that suggested that the audience is the most important thing and you need to know who you are talking to. It is important to consider them and what they know or don't know. Are you preaching to the choir, are you being didactic, are you plugging into the contemporary culture and conversation? The second voice said, forget the viewer (audience). You are the audience for you work. My interpretation of this being that if you can connect with your work, others (like you) will as well. I think the lady who bought "Two Cows Traveling" was having a completely different experience than I anticipated or intended but probably just as valid. The audience is a wild card.
I vacillate between these ideas but find that I mostly lean toward the idea that I am the viewer and there are others who probably think like me or just as interesting as what I intended. I tend to talk about the universal in art, the idea that if you are connecting through something universal to the human experience the work will transcend what you have made. I hope this is true.