Read your local arts and entertainment newspaper. These publications generally come out once a week, such as the Village Voice in New York or LA Weekly in Los Angeles. These types of papers are usually the best source for finding out which local bands are playing and where.
Peruse different blogs and websites about your town's local bands. Sometimes a band or music venue isn't big enough to make it into print, so it's better for you to take the search into your own hands by researching the subject on your own.
Sign up for music websites such as Songkick (www.songkick.com) and Oh My Rockness (www.ohmyrockness.com). These websites are tailored not only to your musical tastes, but to your location, and will keep you posted about upcoming concerts in your area.