Hello Eleanor,
I have spotted several shops for new/used quad and dirt bikes.
One is on the big roundabout on the beginnig of the airport road, just besides the new Bobcat shop.
Another one is close to SOUK AL TALATA mall approximatly 400m to the left, after the main entrance gate.
A new 500cc quad bike costs around 1100 LYD.
My 3 sons are also nagging for one. We must ask for a discounted wholesale price ;-)
Cheers,
Joe