You've got a handful of potential problems there!
In the bathroom where you suspect the buried outlet have a look around for other outlets. Is there any outlet visible near the vanity? NEC requires at least one so a builder generally installs only one. I forget the maximum distance.. two feet? If you do find an outlet nearby the probability of a second outlet buried behind the tile is lower.
If you remain convinced there's an outlet buried behind the tile then inspect from the other side of the wall. Drill a large hole (3/4" or so) and have a look inside. Or, cut out a larger section of drywall. If you find there is indeed an outlet buried there you could fix the situation in several ways. One is to carefully cut the tile and reveal the outlet bathroom-side where it belongs. Another is to remove the junction box, turn it around to be exposed through the non-bathroom side of the wall, and install an outlet there (or a blank cover plate).
There's some chance the tripped GFCI could be in an unexpected place. Newer construction often puts GFCI in a circuit breaker panel. Also carefully check all the other GFCI locations (bathrooms, laundry, garage, unfinished basement, outdoors) for normal outlets that are without power, as well as for GFCI outlets you'd forgotten about. It's less common (and a code violation, I believe) for a bathroom to be tied into a GFCI-protected kitchen circuit.