The Ancient Near East
We follow the first family all over the place in Genesis, but everything goes down in what we call the Ancient Near East or Ancient Mesopotamia. And we're talking ancient—these stories take place probably around the 1800s BCE. Nowadays—millennia later—this area encompasses Egypt, Israel, Palestine, Lebanon, Syria, Iran, and Iraq.
And as it turns out, Genesis explains the origins of a bunch of different places: Shechem (12:6); Jerusalem (here called Salem) (14:18-19); Beer-lahai-roi (16:14); the wilderness around the Dead Sea (19:24-28); and Bethel (28:19; 35:3). The fancy word for this is etiology, and Genesis is full of it.
The geographic center of the story is of course Canaan. The promised land.
One way to think about Genesis-geography is to trace the protagonists who enter and exit the land. Why? Well, they're supposed to possess it (God shoves that one down our throats), but they're all basically immigrants. Abraham and Isaac are forced to go elsewhere when famine strikes (12:10; 26:1), and Jacob flees from Esau to the east of Canaan and then moves to Egypt to escape—you guessed it—another terrible famine.
In Jacob's case, significant divine epiphanies mark his exits and re-entries (check 'em out: 28:10-22; 32:23-33; 46:1-7). The setting dramatizes the tension between divine promise and human reality. And despite all the big promises, the patriarchs remain immigrants, exiles, or refugees until the very end.