Crape Myrtles....come in dwarf sizes all the way up to trees
Ligustrum
Primrose Jasmine
Texas Sage
Burford Holly
Chinese Holly
loquat
Flowering Pomegranate
How about a Japanese Yew in a container
Pampas Grass....cut it back to suit
Pygmy Barberry
Dwarf Abelia
Cotoneaster
Plumbago.....everytime I see that word, I think of an aching back

The big thing still to consider on balconies is the wind.
If your apartment is open to winds of sort, it could play havoc with whatever you put out there. Winds dry soil up much faster than any sun that might be high. More water would definitely be required.

For the window boxes, you might try purslane, portulaca or ice plants - all blooming succulents. They do well even in south Texas (RG valley, grew up there) so they should do all right for you. You could also try bouganvilla, which is gorgeous and tolerates heat and drought and will shade the rest of your area. (You might have to protect it during your winters, though.)

A lot of mediterranian herbs will flourish in your space... rosemary, lavender, oregano, possibly sage and thyme too sinse your area is dryer and has colder winters than us on the coast. Basil will take sun and heat, but it is a thirsty plant so take note.

best of luck!