Check the streets and alleyways. An injured animal may not be able to get home or may choose to withdraw into a quiet place. The sooner the cat can be given emergency care the better its chances of survival. Sometimes cats climb into moving vans or parked cars and are not found immediately. Ask neighbourhood children if they have seen anything.
Children can be a great source of neighbourhood goings-on.
Put up posters around the neighbourhood. Vets will stabilise injured cats before they are taken into the animal shelter. If you offer a reward, beware the hostage-taker or bogus calls. Your description may not be sufficient to help an attendant identify the cat over the phone. Ask if any overflow cats are being held in the dog area.