Try fuschia for the hanging plants. Assuming, since you face south, you get bright light even if no direct sunlight? You could try impatience, torenia, begonia, caladium; all do quite well in bright shade.

Also, columbine, zebra plant (ligularia), ferns of all kinds, pothos ivy, epiphyllum, rhipsalis, asparagus fern.

I do get bright indirect light. However the humidity is usually 90% or above. I think I'm going to try some trailing begonias and ferns. The torenias are a nice idea and I might try them out in the balcony rail boxes.

For a nice potted plant try acuba (I hope I remembered that right). They are normally planted in shady areas of the yard and are evergreen in the south. I have used them as indoor potted plants though.
And what about chenille plant? I'm sure that is a common and not proper name but mine has bright pink fluffy things on it and does best out in the humidity (and shade) in the summer.

Aucuba are evergreen in the north too. ;-) One of my sisters has an old large pair in her yard (male and female gold dust, where the female produces berries every year) and they are planted all around my neighborhood as informal evergreen hedges in part to deep shade.

That's the exact conditions of my front porch, LOL! Nothing's hotter and more humid than Houston in the summer. So, you should be able to grow any of the things that I'm growing, which include:

coleus
calla lilies
English Ivy
Pothos
Wandering Jew
Aloe vera
firespike (some like shade, some need sun--check before you buy)
mint
Persian Shield
caladiums
kolanchoes
spider plants
sweet potato vines (I'm about to be growing them there, anyway, and was assured they'd be fine)

For your French Quarter effect, you can take some of your climbers (ivy or potato vine) and make it grow up your balcony rails to give you a privacy screen. English Ivy, pothos, mint, coleus, and Wandering Jew will all be good for your hanging baskets (you can also use impatiens for color). The rest of the stuff you can just arrange in containers however it pleases you. Most of the plants I listed above do well with cuttings, so if you're on a budget, that's a big plus.

Good luck! : )