Exodus chapters 17 and 18 appear to contain parallel interpolations into an earlier text. In 16:2, the Israelites complain about lack of food and then verses 16:2-36 explain how the Lord responded with manna. In verses 17:1b-2, the Israelites complain about lack of water and then verses 17:3-7 explain how the Lord commanded Moses to provide drinking water. Tzemah Yoreh (The First Book of God, pages 79-80) believes the first of these passages was written by the Priestly Source and that the second (17:1b-2) contains Yahwistic and Priestly material.
For our purposes, whether or not we regard the two passages in which the Israelites complain and are satisfied as interpolations, they can be removed without otherwise affecting the context, resulting in:
Exodus 16:1: And they took their journey from Elim, and all the congregation of the children of Israel came unto the wilderness of Sin, which is between Elim and Sinai, on the fifteenth day of the second month after their departing out of the land of Egypt.
Exodus 17:1a,8: And all the congregation of the children of Israel journeyed from the wilderness of Sin, after their journeys, according to the commandment of the LORD, and pitched in Rephidim ... Then came Amalek, and fought with Israel in Rephidim.
The war against the Amalek commences after the Israelites leave the Wilderness of Sin and is only be conducted by day, "until the going down of the sun". Surprisingly, the Israelites can only succeed while Moses holds his hand high, supported on a pile of stones. As the name "Rephidim" (Hebrew: רְפִידִם) may mean 'supports', it is probably not a real location but an allegory. This then leads to the conclusion the the Wilderness of Sin could similarly be an allegory, rather than a real location.
We now know that the ancient Semitic moon god was called Sin, so the Wilderness of Sin could have been the night, when the moon god ruled. When the Israelites left his domain - when day broke - they fought with the help of the sun.
On this basis, Wilderness of Sin was a poetic description of the night, contrasting the domain of the moon god with that of the sun god, who helped defeat the Amalek. On this analysis, there is no physical place corresponding to the Wilderness of Sin.