I was wondering if any of you have ever found out the name of the ship or galleon that your ancestor traveled on from Europe to Colonial Mexico?

I would assume that VeraCruz was the main port where they docked. But at that time, they would have docked at San Juan De Ulua:

http://www.sanjuandeulua.com.mx/

http://img638.imageshack.us/img638/682/sanjuandeulua.jpg