The art world (around here) can be divided into a few parts: "safe" traditional realism that appeals to a general audience; "literati" art (I'm sure there's a better term), in which the artist explores a unique vision, that appeals primarily to art snobs; and "underground" art, which tends to appeal to the Bohemian spirit. Of those three categories, underground art is the least likely to appear in art galleries, but it is also the one that, in my opinion, best represents true artistic vision and energy.
For much of the twentieth century, Waterbury was a great city for artists. The Waterbury Art School brought instructors up from Yale; the School's students regularly exhibited their works at the Mattatuck Museum; and they spent much of their time in studios on Bank Street. The Mattatuck's Juried Show is now held once every other year and is pretty much the only opportunity for local artists to get any exposure in Waterbury. The Mattatuck also has a regular contemporary art show, but the artists are always well-established in the art world. The Silas Bronson Library has a wall for art shows, but it's little more than a hallway, dimly lit, small and often overlooked. John Bale Books has had a couple of great one-night shows, coinciding with their summer open mic nights, where any artist can display artwork (and it would be great if they did more of that!).
The Artwell Gallery in Torrington is the closest art gallery to Waterbury where any artist, no matter what their style or level of experience, can exhibit. Down in Bridgeport, there's a fantastic cooperative art space called The Nest Arts Factory. They've taken over an old factory, using one room for a gallery, another for music and performances, and other spaces for studios.
Increasingly, the place to find great art in the Waterbury area is tattoo parlors. No Regrets in Naugatuck has an art gallery and regular exhibits. On March 22nd, they're holding a benefit art auction to help fund low income classrooms, with "underground" artworks from artists all around the state and region.
MySpace is also a good place to find local artists. The site has a great setup for musicians, less so for artists, but a lot of visual artists are posting their work on their profile pages.