Tarentola mauritanica; also known as common wall gecko or crocodile gecko.
The moorish gecko is immediately recognisable by its dark grey colour and squat body (as opposed to the more lithe, green wall lizard). Spiky, seemingly armour-plated appearance and serrated vertical pupils make it seem a little dragon-like. The moorish gecko is about 5cm long when born, and grows to about 15cm.
Geckos are also nocturnal, which might explain why you see these less often the lizards, although they do occasionally come out during the day. They're climbers, so look for vertical rather than horizontal surfaces: keep an eye on the dry stone walls in areas like the Appian Way or on larger terraces in the city. They tend to freeze if they think they've been spotted, but look away for a second and they'll have gone.