Natasha likes the night. She honestly does. It's something left over from when her parents were still alive; they'd head out in their small, secluded back yard, and her parents would sing her to sleep. The night would calm them all, and she'd like it. She'd fear it, but she'd like it.
But that was a long time ago. She's been trained not to fear anything, or to get attached to anything. She's a spy and assassin, so anything she knows probably won't stay for long. However, night has no possibility of leaving, so she gets attached to it. It's one of the few conventional things in her life, and she enjoys that. She watches the city at night, and relaxes.
After a while, she watches everyone else's late night exploits.
Tony walks through the kitchen, grabs a coffee and heads to his workshop. She doesn't see him till morning.
Steve sits on the edge of the tower sketching, and she sees no reason to stop him.
Bruce stands on the top of the plaza, never moving.
She never sees Thor.
Whenever Clint is around, he'll always find her.
And the Avengers will sit, unknowing, in companionable silence as the sun rises over the horizon.