if you assume g0=G * M/(R^2) G gravitational constant, M mass of Earth, R radius of Earth, then, if the object's height on the ground is h, you'll obtain g1=G*M/<(R+h)^2> and if you consider latitude, you'll have

g= g1- R*(w^2)*(cos a)^2

where w is the angular velocity of the Earth, rotating on the axis which passes through the Poles and a is the angle from the equator.
If you are at a distance x from the centre of the Earth, with x<R, you have to use a different formula for g1, but I don't remember it.
Sam.