What are the best plants for an east and west facing patio?

Do you want low shrubs or something for privacy?

What Zone are you in?

Watch the balcony for a day and see how much morning and afternoon sun the balcony patio gets and go from there. Since we don't know what zone you are in, I would go to a local actual greenhouse and get their advice on the easy to care for plants that will do well in the light conditions you have on the balcony. If they have printout on the plants care, I would get them to refer to when you care for them. Different plants can have differing needs for water and fertilizing, etc.