The relationship between balance, hearing and eyesight is complex. The nature of the relationship can be the basis of a solid research-based project. One idea for a research project based on balance relative to hearing is to research the biological link between balance and hearing in the air. As part of this project, you look in biological journals and research the part of the ear that is responsible for balance and hearing and try to determine whether a consensus exists on how the two functions came to be shared by one organ.
A project on balance relative to eyesight can research the question of whether any organs used in eyesight are also used in balance. This project would need to draw on research in neuroscience journals.
The easiest experiments on balance, hearing and eyesight deal with a non-impaired person's performance when temporarily handicapped. One project idea is to get people to try standing on one foot for 30 seconds while holding their left finger to their nose (while normal); then blindfold their eyes (or plug their ears) and have them try it again. In both tests, you use a stopwatch to measure how long it takes before the person loses balance. Another project involves testing gymnasts' ability to do headstands with normal eye/ear functioning and then with blindfolds/ear plugs.
Blindfolds and ear plugs cannot give hearing and sighted people the sense of what it's actually like to be blind or deaf. If you want to test the effects of congenital sense defects on balance, you need to get test subjects with congenital defects. One project idea involves getting two test groups, a hearing- or vision-impaired group and a nonimpaired group and getting both groups to try balancing something on their heads (for example, a book) for five minutes. Another project involves giving the members of the groups surveys as to how often they fall down due to losing balance (explain that tripping over something doesn't count).
Sometimes our senses of sight and hearing can be functioning well but under-stimulated due to sensory deprivation. Sensory deprivation occurs when you are in an area with very little light or sound and thus cannot see or hear much. One project on balance, eyesight and hearing in a sense deprived situation involves having the test subjects try balancing on an object in a well lit room and then in a dark room. Of course, when the person tries to balance on an object, you will need to surround the person with pillows because you cannot risk injuring your subjects. If you have access to a soundproof room, you can do the same experiment except in a sound-proofed room to test the effects of soundlessness on balance.