Breaking at the bottom would be the best way for it to break.

A couple of notes: The space elevator needs to have a top at geosync orbit, and a counter balance extending above geosync orbit. You can't use a space elevator to get into low Earth orbit, because at low Earth orbit heights you aren't going fast enough to be in orbit.

Not having the elevator on the Equator is possible, but adds to stresses as there is now bending in the elevator cable.

Now the elevator will be under a lot of tension. If it breaks at the base, the whole thing will lift off and be flung off the Earth, and probably end up in solar orbit. The bottom part will be dragged at high velocity through the atmosphere, probably fragmenting and the fragments will fall in the neighbouring districts. 

If the elevator breaks higher up, the lower part will fall down, wrapping itself around the equator. God help anyone living on the Equator. Although the broken elevator won't hit the ground at very high speeds (thank you atmosphere) it will cause a line of destruction through Brazil, Congo, Indonesia and other countries on the Equator.

These breaks can be simulated: Blaise Gassend has done some animated gifs of an elevator break at various altitudes. http://gassend.net/spaceelevator/breaks/index.html

His model assumes "The elevator that is simulated is an equatorial uniform stress elevator with Brad Edwards' standard parameters. Length is 91000 km, density is 1300 kg/m^3, strength is 130 GPa with a factor of safety of 2, Young's modulus is 1 TPa."