As hip, contemporary, and progressive as Boulder is, it's lacking in public art and theater spaces. The two main players in town are BMOCA (the Boulder Museum of Contemporary Art) and the Dairy Center for the Arts.
The Dairy is a great, large building that houses a number of Boulder's arts organizations. It's central space is an excellent gathering / meeting space that regularly has outstanding exhibits of local artists (and occassionally not so local artists - like my mom - Cecelia Feld - www.studio7310.com). The theater is larger (seats a couple of hundred) and has edgy, contemporary, hilarious, and often excellent shows.
The Dairy is currently being run by Mollie Fager, who does an extraordinary job. If you are a Boulderite that has never been to the Dairy, look for a excute to go check it out.