Both Robert Karl Gnuse and James Hoffmeier deal with the question of the location of Sinai/Horeb. Gnuse, in The Elohist, says that in E the operative phrase is the “mountain of God.” Horeb, he thinks, has become attached to this concept. But the mountain of God is not a particular geographical location. It is whichever mountain God may use for self-disclosure.
Hoffmeier, in Ancient Israel in Sinai, takes the location of the mountain as a particular place much more seriously. He rejects the documentary hypothesis. He says that Horeb is a desert. In fact, the word means desert. The term “mount Horeb” is only used once (Exodus 33:6). It is not the name of a mountain but means the mountain that is in the Horeb wilderness. Sinai is the name both of a mountain and of a wilderness. The Bible definitely uses it sometimes as the name of a mountain. (He speculates that perhaps the Amalekites, who frequented the area, named it that.) More broadly, though, you can say that the Bible uses Horeb and Sinai interchangeably.
Hoffmeier opts for the traditional view that Sinai is in the southern range of the Sinai peninsula. He bases this on the ecology of the region and, more importantly, on the statement in Deuteronomy 1:2 that it was an 11 day journey from Kadesh Barnea to Horeb. A day’s journey was a standard ancient measure of distance. It was based on how far a caravan could go in a day. He calculates that an 11 day journey would be 165-220 miles. This fits the distance from the Kadesh area (understood to be around two oases in northeastern Sinai near the Negev).
I think Deuteronomy 1:2 may be referring to pilgrimages devout Jews made to a place they thought was Horeb. They probably traveled in caravans. However, the Numbers 33 itinerary would be based on travel with livestock, children, and the elderly. By that measure, a day’s journey was quite a bit less than 15 miles. (My fit 18 year old granddaughter is hiking the Appalachian Trail and, depending on terrain and weather, 15 miles is a good day’s hike for her.)
Hoffmeier argues that Deuteronomy 1:2 does not fit the other proposed locations for Sinai.
However, although Hoffmeier has some sound arguments for why the mountain of Moses was not in Midian, surely the Midianites and Edomites did have one or more sacred mountain. Yahweh of Teman is attested in inscriptions. And Egyptian inscriptions tell us of the Shasu of Yahweh in the region of Seir.
It seems to me that Hoffmeier is putting an awfully lot of weight on one verse and what may be too generous a calculation of a day’s travel. I wonder if the Hebrews themselves, by the time of the monarchy, remembered where Sinai was. Maybe Psalm 81:7, which refers to the secret or hidden place of thunder, is telling us that its location is a divine mystery.
A part of what Hoffmeier says goes along with Gnuse’s notion that many mountains might be sites of revelation. He talks about how mountains from Olympus to Baal-Zaphon to Zion were the dwelling places of divinities.
One passage I found particularly interesting. Hoffmeier talks about Mount Hermon, a northern mountain range visible from much of Israel. It was sacred. He says that surveys have identified more than 20 temples on its various peaks. The name, Hermon, suggests a place “forbidden because sacred” (p. 112 of Ancient Israel in Sinai).
Hoffmeier does not mention Psalm 65:15-18 where the “many peaked mountain” of Bashan is surely Hermon. Israel Knohl has an outside-the-box interpretation of this psalm. He thinks the mention of “Sinai” in verses 8 and 17 refers not to a mountain, but to a god, perhaps called El-Sinai similar to El-Shadai. Psalm 68, he believes, equates this God with El. The name got transferred to a mountain later, making this psalm extremely old. The Israel of the Merneptah Stele (-1209) may have been in Bashan and northern Galilee and experienced God as a presence on the sacred peaks of Hermon (see here).