The Terminator is seen breaking into a car as daylight comes about. Thing is, was it up all night at the Observatory and if so, what was it doing? It probably would have had an easier time and earlier start to seek out the Sarah Connors when it was still dark out. It may have been able to even get away with breaking into their houses and killing them.
The Terminator isn't on a schedule. As far as it's aware, there is no opposition to its plan to kill Sarah Connor so there's no point rushing into things half-assed. It gets some money and some clothes, acquires a vehicle and find somewhere to base itself, then sets off to find some weapons before beginning its sweep.
He had come down Ventura Canyon Road in the dark, seeing no cars or people. He had to walk because the chronoporting had fused electrical circuits in a hundred-meter circumference.
So he came down the mountain like an implacable god descending Olympus, the ornamental chains on the dead punk’s heavy boots clanking with each step. Searching.
He had an indeterminate time to locate and terminate the target and therefore could be thorough in acquiring the proper equipment. His clothes were ill fitting, but he would get more later, if necessary.