A* alternatives?

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Jeremy,
If your map is made up of various rooms with doors (or just doorways) between them, then you can have a two-level pathfinding system. What I mean is, first find the shortest path between the rooms. To do this, each room is a node in the first level of pathfinding.

If the character is in the same room as the destination location, then switch to level two pathfinding, which is more detailed with a grid on the floor. Most of the time, once the character is in the room, there will be a straight line to the destination unless your individual rooms are like mazes.

Dividing your map up by rooms is basically the same idea as using quadrants like smilertoo said.