little bit narrow for 'entertaining'.

small apartment balcony decorating ideas --Google this site for some ideas

These areas can be trellised, paved, planted with trees and hedges, furnished with corner divans and ceramic table/stools to maximize seating, and STILL have room for a bistro set and grill. Happy shopping!

I'd get some of those tall and shorter zinc planters (available from a number of catalogues) and put in grasses and maybe a dwarf conifer...this at the end by your bedroom window. If you have electricity out there you could plug in a murmuring water feature, tucked in among the planters, of some sort (granite pillar where water is recycled over it into a basin...that sort of thing); if no electricity, maybe a shallow basin with water and some water plants. Maybe add a very delicate, very softly toned wind chime if the terrace isn't too windy...something soft and soothing. This will create that calm feeling you want. Google "Oehm van Sweden" and check out their very natural gardens for inspiration. You need to do something on the floor...maybe paint the floor a dark grey or tile it if you can (depends on if renting or owning). Then get some small-ish Parisian cafe-style chairs in either a dark neutral or French garden blue, at the most three will fit, and a tiny round table. At night place some votives around for soft, calming light. It's not going to be a spot to entertain dozens for a summer brunch, but it will extend the feeling of the room inside and be calm and easy-care. Have fun!

Aah, tiling in a rental: cheat, and place them tightly, without attaching

HI -- Small space but it can be very cute. I would put down some exterior carpeting or faux turf . Then get a planter that has an attached trellis that will fit on the end . Plants and some vine will help make it feel more private and more room like. Then a small patio set designed for small spaces ,- get folding ones that has a square table with a couple of chairs . Now you can add some color with the rug and some pillows and a few potted flowering plants and lanterns or outdoor light strings.

Just noticed something: Margery, measure that last step against the dimensions for various pavers; you might be able to find something that will work flush with last little step down -save guests the surprise ( I'm reminded of some college get-togethers and a sprained ankle or two....)