"To my right" vs. "on my right"

When it has to do with direction you'll have to use these- I told Alex to come "To my right".

In some situations and context "To my right" sounds more appropriate.

user21497 is correct in that both prepositions are idiomatic and grammatically correct. However, to me, "Alex is on my right," or "On my right is Alex," imply that Alex is standing (or sitting, etc.) next to you, while "Alex is to my right," or "To my right is Alex," could more generally suggest that Alex is somewhere in the area to the right of you, without being adjacent to you. Again, though, both are correct and there is very little, if any, semantic difference.

The way I see it, it is the matter of standpoint. For example, if you are looking at three people in the following order: X Y Z: you would say "Y is in the middle. X is ON the left. Z is ON the right." Because you're looking at them from YOUR point of view. However, you would have to say X is TO the right of Y and Z is TO the left of X.