It's depends on your schedule.. except monsoons you can visit any time..if you want to go during winter, then you will get snowe landscape or If you want to go during summer then you will get green landscape.
but I think you should visit between winter and summer. means mid Feb to mid March.
I think April to June. Bright sunlight packed with windy air in the evenings make for a great vacation in Darjeeling amidst the picturesque surroundings. This time is good for sightseeing and other tourist activities. But, if you want to capture snowfalls, then late September to December is also good.