When he's Nine he takes Rose to see the Rosette Nebula in all it's bright, sweeping glory. No-one would ever know, but one day after spinning across the galaxy together and making one another laugh until they were lost for breath, he'd been filled with such a strong surge of emotion and the definitive thought that everything was just fantastic, he just had to whip her up this beautiful cluster of stars.
He pretends he doesn't see when Rose wipes a tear from her cheek and he continues to lean out of the open doors of the TARDIS with the biggest, most goofy smile on his face to ever grace the universe.
When he's Ten he takes Donna to visit each of the zodiac constellations because he knows that she believes in all of that stuff, and even though he's seen them all a million times and has counted each and every star that shines before them now, he couldn't possibly be bored because the childlike wonder and unchecked excitement that her eyes hold as they fly in between each one could keep him interested for days.
This is friendship, he realises.
Martha, he shows the Dog Star; partly because Sirius is her favourite character in the Harry Potter books (she didn't speak to him for a whole day after that scene in Order of the Phoenix), but mostly because despite all of the other planets and species and cultures he could show to her, Martha was always most in awe of the things closer to home. After he leaves her to carry on with her ordinary life, she sometimes gets out her dad's old telescope and finds it, shining bright and so very far away (yet not so compared to the places she's been) and she'll smile as she remembers how close she'd been to it, once upon a time. So close her eyes hurt from looking and she imagined she could taste the smouldering fire and rock it was made from.
As Eleven, he's floundering for ideas as to what to show his funny little Amelia Pond, the girl who waited. He takes her through eons and light years to be able to visit a strange planet where the grass is violet and the sky is mint green just so that they can sit hand in hand and watch a meteor shower in slow motion.
The tails of the shooting stars are technicolour and the rocks change shape and beside him, Amy gasps and squeezes his hand and he chuckles and then carries her back to the TARDIS hours later when she falls asleep against his side.
The thing about Amy, though, is that she reminds him of home. Her hair is exactly the same shade as the skies of Gallifrey at dusk, her ivory skin shines like it's moon, and her soul, her spirit is strong and adventurous and completely and utterly embodies the citizens of his home planet; reminds him so dearly of his family and friends whom he once knew but have since burnt to cinders by his hand that he sometimes aches to hold her just to feel like he's back there, if only for a moment.
The Doctor may be brilliant, and he may have seen every second of this universe and the next go by but nevertheless: he doesn't like to live his life alone, because somehow the stars always shine brighter when there's someone by his side.
Note: Title from 'fix you' by Coldplay.
I have links to photos of all the stars mentioned if you want to have a look on my profile- credit to their respective owners :)