There is little evidence of public transport here, but taxi or car service is available. The city is a 15 km long line along the highway, so very little is walkable. The countryside around the city (e.g. the highway to Abha) has a large number of police checkpoints to combat smuggling to/from Yemen; police escorts for tourists are common, and not as much fun as they sound.
Best way is to travel in your own car using any navigational device to visit places of your interest, you can also rent a car.