Visit an art museum. One of the right brain's functions is to perceive color. Taking time to peruse impressionist or contemporary paintings at your local art institute not only teaches you about art history, it also initiates creative thought. Evaluating whether or not you like certain images or color schemes in paintings are decisions brought about by your right brain.
Enroll in a dance class or dance at home. Even if you think you have no rhythm, it might not be true. Often if you feel that you don't excel at a particular creative activity, it's because you have more experience with activities that involve the left side of your brain, like solving puzzles. But dancing is an activity for everyone. Taking a dance class, whether ballet or salsa, or even dancing at home for 15 minutes twice a week, can help develop your right brain.
Develop a business model for your dream business. Creating ideas for an operational business allows your brain to perceive on a holistic level. By building a website to showcase your favorite skill or by drafting notes on a marketing idea, you exercise your right brain. It's possible you'll be inspired toward a new career path.
Write a short story or a poem. Creating images through words or verses calls upon your imagination, which is accessed through the right brain. Developing relational concepts like metaphor (when I dance, I am a bird) and simile (dancing lifts me up like the wings of a bird) enhances your creative cognition. These exercises are particularly effective when you work without censoring yourself. No creative idea is wrong or bad unless you tell yourself it is.
Play a game like Pictionary with your family or friends. Such activities not only stimulate random thoughts, they utilize your right brain to visualize images. Drawing and deciphering images--in this case, with a time limit--can enhance other creative abilities like improvising. Though it's important to plan and organize, the ability to improvise when plans change is a universal skill that can also balance your life and reduce stress.