The Maharsha (M’gila 17a), based on this issue, says that Eiver’s Yeshiva must have been located in B’er Sheva itself, so Yaakov really did leave from B’er Sheva. (He suggests that Shem’s Yeshiva and Yitzchok’s Yeshiva were also in B’er Sheva.) This is backed up by Midrash HaGadol using the 14 years Yaakov spent learning in Eiver’s Yeshiva to explain why the Torah tells us again about Yaakov leaving; if his “leaving” specifically refers to leaving Yeshiva after solidifying his learning, and he left from B’er Sheva, the Yeshiva he was studying at must have been in B’er Sheva.
However, if Yaakov was trying to hide from Eisav so that he couldn’t kill him (see 27:41-45), it doesn’t seem to make sense for him to do so right under his nose — in B’er Sheva. Nor would Yeshiva — where Yaakov always hung out (see Rashi on B’reishis 25:27) be a good hiding spot, especially if it was located right around the corner! Even though it’s unclear whether Yitzchok was still living in B’er Sheva at the time — it was his last known residence (26:23-33), but his primary residence was in Chevron (35:27; see http://rabbidmk.wordpress.com/2010/11/11/parashas-vayaytzay-5771/) — if the Yeshiva was right there in B’er Sheva, wouldn’t that be the first place Eisav would look?
Midrash Agadah (28:20) tells us that Eisav sent his oldest son, Elifaz, to chase Yaakov down and kill him, but because Elifaz had studied Torah under his grandfather, Yitzchok, and/or under his uncle, Yaakov, he refused to go through with it. Upon asking Yaakov how he could obey his father’s command without committing murder, Yaakov gave Elifaz all of his possessions, since a pauper is considered as if he’s dead (thereby allowing Elifaz to technically fulfill the orders his father gave him). If Elifaz was able to convince Eisav that Yaakov was “dead,” Eisav wouldn’t be looking for him anymore, so Yaakov could “hide” in Eiver’s Yeshiva in B’er Sheva. A similar Midrash, quoted by Torah Sh’leima (28:97), says the Yeshiva was right next to where Elifaz caught up with Yaakov, so Yaakov was able to go into the Yeshiva right after their encounter. Based on this, it could be suggested that Yaakov only decided to stay in B’er Sheva after being confident that Eisav wouldn’t try to find him anymore.
Moshav Z’kainim (29:1) and Turay Even (M’gila 16b) say that Eiver’s Yeshiva was outside the Promised Land, as Eiver’s “hometown” was “on the other side of the river,” in the “Land of the Eastern Peoples.” Rather than learning in Eiver’s Yeshiva before leaving for Charan (Charan was also “on the other side of the river” in “the Land of the Eastern Peoples”), after crossing the (Jordan) river, Yaakov went to the Yeshiva, spent 14 years there, and then stayed in the general area by going to Charan. However, the Midrashim that mention Yaakov’s “shortened trip” (e.g. Targum Yonasan on 28:10, Sanhedrin 95a/b, Tanchuma 3/8, B’reishis Rabbah 68:8, Pirkay D’Rebbi Eliezer 35) have this trip starting at home (or nearby) and ending in Charan; if Eiver’s Yeshiva was past Charan and Yaakov went there first, the Yeshiva would have been the end point of his “shortened” trip, not Charan. [Seder Olam (2) says explicitly that Yaakov hid in Eiver’s Yeshiva in Eretz Yisroel.] Therefore, although it is likely that Shem and Eiver originally set up a Yeshiva (or several Yeshivas) in their hometown (see B’reishis Rabbah 52:11), by the time Yaakov learned there, they had moved to Canaan and opened up shop there. As a matter of fact, Yitzchok learned at Shem’s Yeshiva (B’reishis Rabbah 16:11 and Targum Yonasan on 22:19), and he never left the Holy Land! [Rivka consulted with Shem at his “house of study” when she was pregnant (Rashi on B’reishis 25:22), and Yaakov frequented the “tent of Shem and the tent of Eiver” (Rashi on 25:27), something that would have been quite inconvenient if they were (still) “on the other side of the river.”]