You might want to check out Cindy's blog FW Dirt. She gardens at an urban loft in Fort Worth. Before moving to Ft. Worth Cindy worked for one of the best nurseries in Texas where she taught classes on container gardening. Urban gardening is her focus now.

Here is a link that might be useful: FW Dirt Blog

I moved to TX in 2008 for grad school and have done a lot of container gardening. What direction does your balcony face/how much sun will your plants be subjected to? That will be important to know what will grow best.

For aesthetics, plants like Mexican heather, Passiflora, Plumeria, and dwarf lilly of the nile have worked well in containers for me.

For functionality, I've had a lot of success with herbs of almost all kinds, okra, peppers, and tomatoes (with a bit of work). Basil and oregano have been particularly great for me in the TX heat/sun.

Best of luck to you and your future container gardens!

Thank you to both MNtoTX and Rock Oak Deer-
I will most definitey check out FW Dirt. Our terrace is North facing. The interior of the apartment is tremendously bright with 11.5 ft ceilings and many full walls of glass. So besides our woefully inadaquate outdoor space, I will have lots of options for indoor planting that I could never have done in the Northeast. (note: I am trying to find the silver lining to this move). I love many interesting non-flowering plants and am hoping to grow ferns, caladium and fiddleleaf figs indoors. Any thoughts?