Have a look at the following web site:
http://www.tungsten.com/mtstung.html for a very useful table of the properties of tungsten.
The very high melting point compared with something like steel (1700 oC) or copper (1356 oC) means that it can withstand the high temperatures needed to give out sufficient light. The temperature of the filament in a light bulb is some 1800 oC.
It has a very low vapour pressure which means that even at high temperatures the light bulb is not filled with tungsten vapour.
It also has a very high tensile strength at the temperatures in the bulb. This makes it well able to withstand the thermal shock when the light bulb is switched on.
Important properties therefore: low vapour pressure, high tensile strength, high melting point.
Tungsten is not a 'good' conductor for two reasons:
(a) fewer free conduction electrons than, say, copper
(b) a large amount of electron scattering from the tungsten lattice .