I'm kind of new to this too, but I would think you could do some hearty stuff like lettuce, arugula and kale. Are you sure it only gets one hour of direct sun? It seems like even a north facing balcony would get a few hours..

I'm not 100% certain about the one hour thing. I said it because the maint part of the building is on the south side, and there is only a slice of sulight that moves across the patio wall in the morning. Any single area only gets about an hour before the light moves on. I'm not typically home in the afternoons, but there may be a sliver of direct light there too.

I love kale... what sort of soil/pot requirements would it need?

If your balcony only gets an hour or two of sunlight I would forget vegetables and go for flowers. Impatiens bloom under such conditions. Hostas would also survive and give you nice greenery and a brief flush of summer bloom.

Sweet cicely is a lovely herb with fernlike foliage and a long season. It tastes like anise (licorice) and is nice chopped in fruit salads, pies, teas, etc.

Sweet woodruff is a very pretty shade-lover than bears small white flowers in the spring. Its umbrel-shaped leaves are good as pie decorations or in punches, and dried they make a fresh-smelling, long-lasting potpourri.

Asarum is a ground cover with pretty, dark green leaves that produces rhizomes (roots) that taste like ginger.

For a few other ideas, check out Tripple Brook Farm. You can browse, or do a plant search by properties (such as Edible and Shade).