So, to start:
Shiro only gets like four hours a night, at best. He usually paces the halls and when he does get rest, he's tossing and turning from nightmares. He's found that he sleeps better when he's with someone to help him with night terrors. Usually, he works out in his quarters until it's time for breakfast.

Keith sleeps like a log. He lays on his back with his arms by his sides and his legs together, and he. Doesn't. Move. He's confused by the idea of ever falling out of his bed while asleep, and doesn't understand why Lance seems to have that problem.

Pidge doesn't sleep, it seems. Every time anyone goes in her room she's on her laptop and eerily alert. Lance is a little creeped out by it. (She usually falls asleep by her computer.) The first time Lance saw her taking a nap he freaked out and called Coran, thinking she had died. This earned him a few choice words from Pidge and a confused chuckle from Coran.

Lance QWOPs. He's like a starfish, and he loves to hug a pillow (or a person, if it's offered to him). The only time he's still is if he has someone else with him. He makes sure to get enough sleep to stay looking gorgeous, and he values relaxation very much.  He's also fallen out of his bed multiple times.

Hunk lays still most of the time, though he does move during nightmares. He gets a pretty good amount of rest and he doesn't have much trouble falling asleep. He usually tells Pidge to sleep before he goes to bed himself, and he gets up early enough to make breakfast. He loves doing this for the other Paladins, and it makes their mornings much brighter than they could be.

Allura sleeps a great amount for an Altean. She usually sleeps for only a few hours before wandering the halls and having conversations about battle plans with Shiro in the middle of the night.

Coran???? Never sleeps???? Nobody knows where his room is and he seems to be everywhere at once. He especially enjoys going to tidy up the castle and carousing old parts of the castle while remembering the past.