When installing hardwood flooring, there are a number of ways to meet up with a doorway, tiled entry, or tiled hearth. In many instances you can avoid using a raised transition by using pieces of flooring.
For tile, install the boards around the tile like a frame. Then begin installing the flooring, starting at the frame and working your way out across the room.
For a doorway, install the board in the doorway. Then run the boards out from it perpendicular to the transition. This provides a smooth transition and creates a little point of interest too.