Hardwood to Tile Different Height Transition
That's a difficult one, and probably should have been thought through before installing the tile, not after.

I like using stone thresholds (commonly marble or granite) to terminate tile, but even a 6" wide would be sitting at a steep angle to make 3" vertical offset, and still be a stumbling hazard, at least. I'd probably take out that last/first tile and chew downwards until I could set it as a ramp of more reasonable slope. 

If you are just going to have a 3" step and hope not to fall on it, you could make one from wood, or you might be able to set a 2" stone threshold on edge and a 4 or 6" one flat on top of it, filled with mortar to make the step; Or, remove wood in the threshold area until you can fit a solid 3" thick stone in there flat.

Alternatively, build up a ramp on the wooden floor side.