Elijah is on a journey to the eternal land of God’s rest.
He starts in Gilgal, which is a throwback to Egypt. At Gilgal “the shame of Egypt” was removed (Joshua 5:8-10), when the foreskins of the Israelites were taken away.
Bethel is a throwback to Sinai, when the dwelling of God came to earth. (The Shekinah was the dwelling place of God.) Bethel in Hebrew means the house of God.
Finally, after the Israelites left Sinai, they had circled the wilderness before arriving at the River Jordan. Jericho therefore was a throwback to the (circular) wilderness wanderings, where the desert was a place of death and unfruitfulness (2 Kings 2:22). Joshua had circled the city before destroying it.
Thus Elijah makes a trek to follow the pattern of the Israelites who left Egypt and finally entered the rest of the Promised Land. Elijah therefore followed this earthly pattern in a reverse imagery (if you will), so that when he crossed the Jordan he entered the rest of the heavenly Promised Land.
By asking Elijah to remain in each locale, Elijah was essentially testing Elisha, since Elisha was his protégé. (“Would Elisha remain in ‘the wilderness of Zin,’ or would he proceed forward to cross the Jordan as an obedient Israelite?”) Of course, Elisha wanted to follow Elijah wherever he went. Elisha passed the test, and therefore was qualified to replace Elijah.
After Elijah was taken into heaven, Elisha “returned to earth” by back-tracking the same steps. (Elisha made the “death and unfruitfulness” of Jericho’s “desert” into potable water in 2 Kings 2:22). He goes through Bethel, where (like at Sinai with Moses) insolence and insubordination was evident toward God’s prophet, Elisha (2 Kings 2:23). As his final destination, instead of returning to “Egypt” (Gilgal), he returned to Mount Carmel, which is where Elijah’s ministry had ended, and where of course Elisha’s ministry was going to begin.
Theologically, this whole episode of Elijah crossing the Jordan and entering heaven is of immense significance hermeneutically. First and foremost, this is the first instance within the Hebrew Bible that there is direct parallel between the visible "rest" of God and the invisible "rest" of God. In other words, the biblical concept of "the Promised Land" (God's place of rest) is not limited only to the visible geographical area of Palestine, which was promised to Abraham.
For example, the author of the Book of Hebrews enters his theological discourse by indicating that the "rest" of God follows death (see Hebrews Chap. 3 and Chap. 4, where the concept of the afterlife is developed from the Hebrew Bible). In other words, when we depart our terrestrial existence on earth, we "cross the River Jordan" and enter the rest of God. (Death is not a "dead end" for the elect of God.) Many 19th century church hymns talk of this crossing. For example, when he died on the battlefield during the Civil War in 1863, Stonewall Jackson is said to have remarked, "Let us cross over the river, and rest under the shade of the trees."
Last but not least, Elijah did not experience physical death. He went into heaven, and therefore heaven is a literal place. Later in the Hebrew Bible (in fact among the last verses of the English translation of the Old Testament), there is indication that Elijah will physically return to earth "before the great and terrible Day of the Lord," and so there is still an expectation (among Jewish and some Christian students of the Bible) that this Prophet will yet return to earth physically in the future. While Malachi 4:6 is attributed to John the Baptist in Luke 1:17, the verses in both Malachi 4:6 and Malachi 4:5 also seem to point to "Elijah the Prophet," who will return to earth "before the great and terrible Day of the Lord" and announce the [second] coming of the Messiah to earth.