Taking the core to be a point, the distance to the sea's surface would depend on factors such as
* The earth’s variation from a pure sphere (6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles) [0, 1]
* The local depth of the sea (up to 10,984 metres for the Mariana Trench [2])
* Tidal effects [3]
[0] https://en.wikipedia.org/wiki/Spheroid
[1] https://en.wikipedia.org/wiki/Figure_of_the_Earth
And correct me if I'm wrong, but the local depth of the sea should not matter, as water would fill the depth before the levels stabilized. But perhaps the local volume of the water affects the size of the effects of tidal forces and local land mass.