A closer pic of the 'soil' quality

From above - the 'back yard'

Hi. Bit of a yuk really! The area looks rather narrow; fence, then concrete: blasted by the sun and a micro-climate of reflected heat. I think what I'd do before I planted anything would be to check the moisture content of the soil (I reckon it'd be low - don't let the grass and weeds be a guide - some weeds'll grow anywhere). Also have a dig here and there to see what's just underneath, rocks, sand, for example. If it's just plain ole reasonable soil, then before planting anything I'd fork in some water retentive crystals and 'Trace Elements'. Bit of compost-come-fertiliser would also be beneficial. As for plants: Jania (a very drought resisting creeper with yellow annual flowers); Uvolulus (also very drought resistant, blue flowers through summer), maybe dwarf crepe myrtle but than can sucker and suffer from scale; and cactus and some succulents might be worth a little consideration.
B.

Where abouts are you? Knowing your climate would help.

The Mother-in-law's Tongue in the first photo should be okay in that situation, they're a "cast iron" plant, except for too cold and/or too wet. The grass seems to be coming from under the fence, it'll be a constant job to keep that under control.

The main weed in the second photo looks like Tridax Daisy, or Singapore Daisy, bit hard to tell from that photo. Tridax Daisy grows well in the poorest soils and harshest conditions, Singapore Daisy likes soil and conditions a lot better. The growth habit suggests Singapore Daisy, so improving soil there would make it really take off and smother everything around.

Generally though, what will do well in your situation will depend a lot on your climate.

I would forget the sleeper idea, apart from the support angle the water from the garden will probably eventually seep thru and rot the bottom of the existing fence.
You have 2 problems there, the harsh aspect as funnelweb said, and also the narrowness of the driveway.
I'm assuming your clinic clients will be offered parking in the rear, and nothing puts people off more than a difficult access. Esp if they have no turning space and have to back out.
If it were me, I'd rip out/poison the rest of the grass down the fence and get some with some cheap gravel to fill up to the fence line.
If the owner consented (and there were no problems with overspray into the neighbours) I'd consider painting that driveway fence - that might be something in a cooler colour or even something linked to your business colour logo. You might even find (through Police Boys Club or similar) a couple of reformed graffitti artists to do you an el cheapo tropical style mural. When you go, all it takes is a another coat of paint to erase it.
A couple of feature pots at the entrance and round the back to link it - as FW said, succulents might be the go- those euphorbia millii poesean plants are very hardy and long flowering, as are bougainvilleas, once established.
You might even be able to do some hanging baskets down the driveway but higher up, on pickets in between the existing fence posts.
Have a look at where your back taps are and see if you could rig up a poly watering pipe along the fence with some drip feeders.
Round the back I think you have a lot more scope for a mini-oasis that both you and your clients can enjoy but unless you have a long lease, I'd be going for a potted garden and and maybe a bark base, BBQ and table and chairs etc.
Your experience, and unfortunately your finances, also come into it.
Would also like to know where you are and which direction the property faces.

Hi thanks for the responses.

We live in Brisbane (Australia). So... humid and hot summers and relatively mild winters (no frost). The direction of the photo along the left fence is north.

I like the ideas posted so far thank you. One of the biggest issues is how to fill the area with gravel/bark right against the fence as its already falling down (at least on a lean). The driveway next door is lower than the lowest point of of the existing rubble against the fence. I suppose bark is relatively light though.

An ideal solution would be one where we can somehow fill in but stop the fill from escaping the gaps in the fence and running into the neighbours driveway... At the end of the day a filled in strip with bark/gravel and potted varieties looks better than over gown weeds.

Hmmm, gravel would be better than bark though as bark will blow around and wash around in rain - and I see you have a stormwater grid down the front that it could all go down.
Any chance you could post a pic from the "other" side so we can see the neighbour's view of the fence and their driveway? and how far below your driveway level do you reckon theirs is and if you have some good pics we can see where their driveway goes to up against the fence and whether there's any sort of retaining wall on their side.

Here's the other side. I reckon the gravel/dirt sits a good 100-200mm higher on our side of the fence at the lowest point.

You can see right towards the back just how far the fence is starting to lean.. not sure about fencing law legalities but its quite a lean!

Taking another look at your pics, can you tell us if that pavement (on your side) is concrete or tar - in one of the pics it looks like tar. If it is you might be able to neaten up the edge, you should be able to do that by hand, you can melt it with a blow torch but you may not want to go that far. I think I'd just cut or break away where the edges are untidy and backfill with soil. Also in your second pic there appears to be a lot of stones or gravel, shouldn't be a problem to clear that away. In your first pic I'd also be inclined to get rid of the sanseivieria (mother-in-laws tongue) and maybe try the tough, blue flowering convolvulus (misspelt as Uvolvulos in my first response). That's a pretty, easy to grow and to propagate creeper. It grows well at my pace at Tweed Heads so it'll go ok in Brisbane. And it's also very drought tolerant.