Here are some other words whose denotation, like that of door, is “opening or passage through an obstacle,” and some notes on their possible connotations.

door a movable structure used to close off an entrance, typically consisting of a panel that swings on hinges or that slides or rotates. Generic term
doorway opening to a room, building, or passage – it may or may not have a hinged door installed. For example, a character might be in an unfinished house or a ruined house with “empty doorways.”
portal a doorway, entrance, or gate, especially one that is large and imposing.
passageway  an extended entrance, like a corridor. The word could be used to imply initiation.
entrance a means or point by which to enter. Generic term.
entry a means or place by which to enter. Possibly fancier than an entrance
entry-way a passage or opening by which to enter. Like doorway, an entry-way may or may not have a door attached.
opening an open space serving as a passage or gap. The opening to a cave, the opening to another dimension.
gate a structure that can be swung, drawn, or lowered to block an entrance or a passageway. A gate is usually out-of-doors, but not always.
exit a way out