Any climbing vines, Charles. The first one that comes to mind is Morning Glory.
Or try something like Baltic Ivy which is year round and often seen climbing up chimneys. This would have to be planted in fairly large dirt planters on the balcony depending ono where you live. This would also need a permanent trellis to climb since it will remain up all year.
Here are tons of ideas for you Charles. Good luck!
What about making a screen out of shutters? Faster than waiting for plants to grow! :)