Plants! Socially, it's a talking point and it makes you feel like you are in a soothing space not just a neglected outdoor courtyard.
Research "courtyard" or "urban" gardens online - you will find a "small" garden is still way bigger than what you have.
My several experiences of new builds has made me learn by bitter, expensive experiment that the ground is often appalling - turf laid straight onto rubble ground, on a plastic green mesh that is a bane to try and dig borders into.
I strongly recommend that you attempt to dig a hole about 50cm deep somewhere near the house, and then again at the end of the garden, so see how much topsoil you have. And bear in mind, the site could have been levelled with hardcore so it isnt a guarantee that the soil is the same everywhere in your garden.
If you are coming across a lot of stones, pebbles, grit, sand or clay, then you are going to struggle to plant in that garden. You should think about building raised beds - these can look amazing if you build them into a seating area.
Don't buy expensive plants until you know the garden better. Planting a lot of lavender en masse, this works brilliantly in poor
soil and hot conditions, and the little mounds looks cute in winter once you've pruned it back in autumn.
Also try planting cistus- the white flowered variety is lovely - which wont mind dry soil and full sun.
If you want to try and get some bigger planting done in the ground, go for a Sambucca Nigra (grows easily and fast, you can't mess it up when you prune it as it is very tolerant of hard pruning, very beautiful flowers and foliage - and cheap!) And red robin, which has lovely foliage and grows easily. I have both red Robin and sambucca nigra at 12 foot tall in my garden - I plant them wherever we live and I've never had a failure yet.
I'm neutral about a lawn. If there is already grass there, you will know how well or badly it is growing. If it is not growing well, replacing it is unlikely to help unless you invest significantly in preparing the ground and maintaining it. You can do wonderful things with areas of paving and large areas of planting and raised borders. HOWEVER if your house is a "family house" bear in mind if you sell it, people might be upset if there is no grass. So it depends on the kind of house it is, and whether you are likely to sell it (or have kids yourself).