Serene--the dictionary says, means calm, tranquil and Serenity is the state or quality of being calm.
Now, to me, certain places make one feel calm , but certain people have that quality too and that is what some saintly people seem to radiate. There is also, always, music that makes one serene.
Places that make me full of serenity--the seaside, especially at night, with the sound of the waves, walking in the mountains, being out on a dark, clear, star-filled night, watching some living being going busily about it's business, an empty church--all these give me a feeling of calm. Also, having a cool shower on a hot, sticky day, lying on a comfortable bed after a tiring day, drinking a tangy lime-mint drink in the shade, with the breeze blowing, having a baby sleeping on my shoulder (provided I'm sitting in a comfortable chair), watching a boat making it's way down a river or into the sea, all these too make me feel serene.