This article is by Clint Watson, former art gallery owner/director/salesperson and founder of FineArtViews. You should follow Clint on Twitter here.
A good art gallery, like any business, must market their product brands, in this case, artists. Building the name of an artist is just like building the name of any good brand. As an artist, your name IS your brand.
Therefore, you want to be in a gallery that HELPS you to build your "brand name." Unfortunately just as the White Whale eluded Ahab, good galleries seem to be evade artists.
I think the best way to look for galleries is to see which ones advertise regularly in the art magazines. I prefer this method, because the ones who advertise are showing SOME effort to market themselves to the target audience of art collectors beyond just the old "sit and wait" routine.
However, galleries in high traffic tourist areas like Santa Fe, Laguna Beach, Carmel, etc may not always NEED to advertise, so they could be exceptions. You could also get gallery guides from those high-traffic art destinations.
Ask artists friends about galleries they are in, particularly artist friends who are further along in their career than you are. They will have advice about finding good gallery representation.
And above all, have a healthy and realistic view of art galleries. If you partner with a good gallery, it can be a good experience, but YOU must still participate in the marketing of your work. I can assure you that one gallery alone will not have the resources, time, or motivation to handle ALL aspects of the marketing of your artwork.
Software Craftsman and Art Fanatic
(and former art gallery owner)