From my experience artistic women like deep thinking men. Driven men with passion and vision. Men who march to their own rhythm. Men who understand what rules apply to them, and know-how to create new rules when the ones they have been given don't make sense to who they know themselves to be, or what they see to be true about the world. Men who can offer a doorway into new perspectives and ways of looking at the world. Men with the ability to turn the mundane dregs of life into vibrant moments of beauty imbued with meaning. Mysterious men who aren't always easily grasped.
Just a short list out of what is no doubt a tome's worth of ideas on how to be this sort of man
-Deep self-reflection. Really search to understand yourself and your experiences. Spend time alone with yourself
-Look for beauty and meaning in everything. Search for a deeper story in even the most mundane moments
-Go on daring adventures. Live just close enough to the edge that you can get a good peek over the other side (no need to be reckless though)
-challenge yourself and your worldview. Put yourself in new challenging situations
-Do things people normally wouldn't do to see what perspectives it might offer (lay down in a puddle on a rainy day, walk across town barefoot, walk backward through a crowded market, sneak into abandoned buildings, sleep on a rooftop somewhere in the middle of a city)
-Find ways, both big and small, to bring a sense of beauty and wonder to others
-Develop artistic abilities
-Study great art and music deeply. Seek to understand the deeper context and meaning with the art you engage with. Learn how to articulate your thoughts and opinions on art in an approachable, non-pretentious way.
-Become deeply observant of the world around you. People, places, things. Look for things others might miss. Share your observations, and show others a piece of the world they may never have even considered.
-Have the courage to stand by what you know to be true regardless of whether others understand it or not.
-Have private pieces of your life you regard as sacred. Places you go that few people know about. Thoughts you only share with you're closest companions. Thoughts you share with no one. Personal rituals that add meaning to your life
That being said, all these suggestions are more just ways that one can end up bringing something to the table that you two might find similarities in. You don't necessarily have to be artsy yourself, but you do have to at least understand where she is coming from. When it comes down to it, game is game. No way around it. And also, don't get so bogged down with deep things that you don't know how to just let go and have fun.
What
@uriel said about them being sensitive and often surrounded by a good amount of partying is pretty accurate. There can be a lot of vanity in the art world, as well as hedonism. This is not true for all artsy women though and they really can run the spectrum of lifestyles and social dispositions. Expect a good majority to be on the typical super liberal "Artsy girl" trip.
Places to meet artistic women?
Coffee shops
Health food stores
DIY venues
Art schools
Art conventions
Cities known for their artistic culture and history
Concerts
Gallery openings
Book stores
Art supply stores
Thrift stores/ vintage clothing stores
Record stores