...you are not trying very hard. Here's a short list of things I am aware of, I am sure there is much more to choose from.
Blues: Friday Night, June 1 is the annual Black-eyed and Blues Fest in Bushnell Park, sponsored by Black-eyed Sally's. ABSOLUTELY FREE. More info....
Alternative Rock: A plug for my friends at Little Ugly - they are playing the Firebox Restaurant (at Billings Forge) on Friday @ 9:00 pm
Poetry: This is the kick-off weekend for the Sunken Garden Poetry Festival, at the Hillstead Museum in Farmington. Poetry and music all weekend long, starting Friday night.
Spirituality: Something new this year, the 2012 Creative Spirituality Fair, in East Haddam is going on Saturday. June 2. All sorts of yoga, healing modalities, energy work, music, arts, food and fun.
Queer Film Fest: The annual Gay and Lesbian Film Fest - Out Film CT - starts this weekend, at Cinestudio. The festival runs June 1- 9, with some big social events planned for apres cinema on the opening night, closing night, and mid fest. A lot of interesting looking films, with several premieres.
Krishna Das: Kirtan and workshop on Sunday, June 3 in West Hartford, sponsored by West Hartford Yoga.
That's just a start, bet there are many more events happening as we kick off the first weekend of the summer season. Get out there and enjoy!