I have an apartment facing west and only get afternoon sunshine.

If your balcony door that is a sliding glass door I still stand by the idea of bringing in extra light with mirrors (even a large wall mirror on the wall opposite the doors so plants could get light from both west AND east). However if you have a standard door opening on to your balcony, I just don't know what to suggest at this point. I am sure not going to give you advice that could get you evicted for having plants on the balcony ;) I hope you understand that. Housing is so much more important than having a small garden that isn't allowed :)

I don't think that's what is worrying them. It's the excess water that will drip onto other peoples balconies. I have 3 small herbs growing on my table on the balcony, but when they get bigger I will need to plant them into a garden. Do you have any idea how to build a raised garden bed on a balcony?

Thank You, but I would truly like to grow an outdoor herb, vegetable or flower garden on my balcony.