“went to Beer.” The word “Beer” means well or cistern, and there were lots of them. The location of this Beer is unknown.
“away from the face of Abimelech his brother.” That is, away from Abimelech’s anger. Some versions nuance the text to, “for fear of Abimelech,” and that is the basic idea in the verse. The Hebrew can also be translated, “because of the face of Abimelech his brother.”