I know that "da" may mean to/at, when someone is talking about "one's place/home" or "one's work place", as "chez" in French. Examples:
Devo portare il piccolo Luigi dal pediatra. (I must take the little Luigi to the pediatrician)
È da sua madre. (He is at his mother's)
However, I have just heard "Venga da me". I thought it would mean "Come to my place", but it was translated as "Come to me". Can it mean both? Is "venga a me" not usual?