Of course the gravitational slowing down of the earthbound observer’s clock would depend on where he/she was on the Earth’s surface. Some locations have a higher level of gravity than others. It depends on the density of the rock below. Also, near the equator, there is an outward force (acting in the opposite direction from gravity) due to the spinning of the Earth (about 900 miles/hour at the equator).
Hmm, again I don't know for sure : ) First off the spinning of the earth doesn't affect the warping of spacetime (gravity) so the equator example seems to be wrong.
The more interesting question to me would be what would be the clock speed for a clock in the center of the earth where it would 'feel' no gravity. It is at the bottom of a gravity well so I would expect that it would be very slow, but it might be that the balancing of gravitational forces at that point produces a 'peak' in the gravitational field, counteracting the other warping?
Always keep in mind that every observer will see his clock running faster than other clocks which are moving with respect to him.