What balancing exercises can I do while seated?

Sit on top of a stability ball. Once you have found your center of gravity slowly raise one foot, keeping your foot a few inches off the floor. If you start to wobble, perform a toe tap to regain your balance. When performing this exercise be sure to tighten your abdominals and sit with ideal posture (no slouching). As a progression of this exercise, you can simultaneously move your arms in multiple directions (front, side, overhead etc.).

The floating chair is excellent to improve balance and will strengthen your lower abs while you are at it. 

Come into a seated position with your knees bent and your feet flat on the ground. Take your hands and grab underneath your legs above the backs of your knees. Pull your stomach in and lift your feet off the ground and balance. When this is easy for you, try to do it with your palms up one inch from the sides of your knees. Hold for 30 seconds keeping your back straight and breathing normally.