Answer: With a balcony situation and in the city, a frequent problem is wind. Wind is very drying and so you may need to consider protection from that when setting out your plants. Another consideration is that afternoon sun can be very hot, especially when reflected off a building. Again, this is drying and also stressful. Using large containers and possibly including the water holding polymer crystals in the potting soil should help.
You should be able to grow any sun-loving veggie, annual or perennial in a container. Try tomatoes, peppers and, if you have the room, squash. There are lots of dwarf fruit trees available and they are naturals for containers. Try apple trees, especially the columnar types that grow virtually straight up with very little branching.
For more hints on container growing, you could search the Q&A and library archive for the specific plants you are interested in or take a look at a book or two about container growing. One I particularly like is Container Growing for Dummies by Bill Marken, Dummy Press, ISBN: 0764550578. In it there are many useful tips as well as general instructions about containers, a variety of plants including vegetables and herbs and also very important, the finer points of potting soil.
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