What factors determine where an aircraft can dump fuel?
Fuel dumping was regulated by FAA Order 7110.65P - Air Traffic Control, which was canceled in 2006. FAA has the following to say regarding fuel dumping:


  ...If the need arises, aircraft are instructed by Air Traffic Control to dump fuel at high altitudes as far away from the airport or any populated areas as possible.


At present, there are no hard and fast rules (at-least in US, for other countries, see below) regarding fuel dumping and it is left to the air-traffic controllers to guide the aircraft. 

The main criteria in determining an are for fuel dumping are:

-Altitude In general, fuel jettisoned above 5000 ft will vaporize before reaching the ground. Due to this, some manufacturers recommend fuel dumping above 5000 ft. In general, the ATC will guide the aircraft to an altitude where it can dump fuel so that it vaporises before reaching the ground.

-Atmospheric conditions The evaporative characteristics of the fuel dumped depends on the altitude and the atmospheric temperature. The aircraft fuel tends to vaporise faster in a warm day.

-Aircraft separation The ATC will try to keep a minimum lateral separation (~5 miles) between the aircraft dumping fuel and other aircraft and also some vertical separation (~2000 ft, according to Order 7110.65P).

Except in case of safety emergency, the fuel dumping is carried out at high altitudes.

Note: Some countries do have fuel dumping regulations, like Switzerland, which says,


  The choice of the dumping area is determined by the urgency of the incident, the actual flight path, meteorological conditions and the general air traffic situation. The aircraft is led to a selected area by the air traffic control to dump fuel. At the minimum speed of 250 knots at an altitude of 6,000 ft, but usually with 350 knots at 14,000-16,000 ft fuel is dumped ... There exist no predefined dumping areas ...