Yes, "Whenever the sun is shining in your town" is a fragment. It does not complete the thought.
Some examples of a complete sentence would be:
"Where"
The negation of the sentence the sun is shining would be that the sun is not shining.
Shining Sun was created in 2010.
Sun Is Shining was created on 1999-09-13.
When all Hydrogen on Sun is finished it will stop shining
The sun was shining brightly in the sky.
Sun Is Still Shining was created on 1969-11-21.
shining
50% of the sun is always shining on every body in the solar system.
Behind the Clouds the Sun Is Shining was created on 1925-11-10.
There is never a time when the sun isn't shining. The sun has been shining for four and a half billion years and will continue to shine for [it is assumed] another seven and a half billion years.
the sun is like a shining bulb