Working on ankle mobility will help balance. Stiff ankles get in the way of maintaining balance so we sat on our feet to open the ankles, did some variations while sitting on our feet, and then tried some balance poses with the chair before doing them without support.
Sit on feet (vajrasana) with feet pointing straight back, feet crossed at the arches, feet sickled with big toes touching, toes turned under with soles of the feet parallel to the wall
Adho Mukha Svanasana
Modified Boat pose
With a chair behind you, sit down and stand up without the aid of your arms. Do with feet parallel and then cross one leg in front of another. Switch the cross. Practice this with different heights.
With a chair or a pile of blankets behind you, stand in tadasana. Go to uttanasana to malasana to paripurna navasana (on the chair or blanket pile) to malasana to uttanasana to tadasana.
Ardha Chandrasana with a chair, then a block
Virabhadrasana III variation with a chair, hands on seat, lifting one leg, then arms
Sirasasana (intermediate only)
Salamba Sarvangasana or legs up the wall