I think it is quite fun to think of the birthday as a time where you are closest to the place in which you were born. This, of course, makes the actual date of your birthday irrelevant, as you have to take leap years and the $6$ hours desynchronization thing into account, but it is still very easy to calculate, just add $6$ hours to your time of birth every non leab year, and subtract $18$ every leap year to figure out, with much more precision, this moment of closest approach.

However, something much more challenging, and much more interesing, in my opinion, is figuring out exactly **where** you were born, and calculating in what direction, and how far that *where* is in the moment of your closest approach birthday, just so you can impress your friends by pointing at a direction and saying "Look! I was born there, about $5$ Earth diameters away"

My question is: What do you have to take into consideration to get a reasonable degree of precision, say $15º$ or less in the direction you need to point? Is it enough to just assume the earth is arround the same position and just see how much the rotation is different? Do you have to account for the precession of the Earth's orbit? And how about minor effects like Milankovich cycles?

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