Rail planters had occurred to me as well.

Once you get some ideas, Tara, before buying anything my suggestion would be to make some cardboard cutouts of the "footprint" each item will have. So if you are looking at a round table with a diameter of 3ft and two chairs each with a footprint of 4ft x 4ft, then make a 3ft diameter round cutout and two 4'x4' square cutouts and place them on the balcony. Do this with any planters, grill, extra chairs or other items you were thinking of having on the balcony. Should you go with the Japanese Red Maple idea, make sure your cutout instead matches the spread of the tree. (Since the tree could be pruned now and then, go with how big a canopy you'd like the tree to have for the cutout. To get some idea -- if you aren't sure -- visit some nurseries that sell trees and take some measurements of the spread of the branches on ones that seem in keeping with what you think would work for you.) Do something similar with any pots and planters as plants will be unlikely to stay within bounds of the pots. Once "armed" with those cutouts, start placing them on the balcony -- starting with the items you find most important/desirable. While somewhat tedious, I know, it will give you a better idea of just how much will actually fit on your balcony and allow you to get some idea of where on the balcony each item should go.

TG's idea of having some screens to block off the view of the parking lot or of the neighbors on either side of you is worth considering as well. Depending upon what your apt/condo complex allows, you might be able to attach the screens with zip ties to the balcony railing for extra stability. Additionally, you would not be damaging the railing by drilling/nailing holes in it and zip ties can be cut off to move or remove the screens down the road. If you get one of the more decorative wood lattice screens and are able to stabilize it, you could even hang some small plants on the lattice.