My orthopaedist gave me leg-strengthening exercises for dodgy knees, which double as balance exercises if you don't hold on to anything. Stand straight, engage core and buttock muscles, and lift each leg in front of you, keeping your thigh parallel to the floor and your lower leg down at a right angle. Hold for count of five. Repeat with other leg. 10 repetitions each, three times a day, or however many you can manage.