Having offered him the gift of water, those two descendants of Raghu wended their way in that forest in quest of Sītā and proceeded towards the south-west*. In this sloka west is mentioned and in the next one there is reference to their turning to the south and hence west here refers to south-west.
कृत्वैवमुदकं तस्मै प्रस्थितौ राघवौ तदा। अवेक्षन्तौ वने सीतां जग्मतुः पश्चिमां दिशम्॥