That was the sort of man he was in the end, terribly impulsive and terrified of being alone. He trusted his instincts, however, and his instincts said she was the sort of rare person he'd be delighted to have as a traveling companion. Not that he would get to do much of the sort while the TARDIS was in a state of disrepair. When he did get it remotely functioning, what then? Where would he go? That was a conundrum for an older version of him, one that wore bow ties had...
Well, he didn't want to think about it. One day a time.
Listening to her reasons, the Doctor continued to smile, this time appreciatively. Those were all things he would have taken into consideration, of course. He had with Rose once upon a time, intended to bring her back as though she'd never really left, but that hadn't worked out in the long run. The more Sam spoke of her family loyalties, loyalties he would never attempt to trump, the more foolish he knew he was for even having posed it. Brushing those thoughts, the Doctor cleared his throat like it was his mind affected and nodded rapidly.
"Yes, no, I don't travel with family if I can help it, only for the appropriate reasons. That said, have I mentioned she's a time machine? When she's working, of course. Won't be going on any adventures anytime soon, as you can see, but if I do manage to connect her to this universe somewhere, well--that's that. Does anyone in your family enjoy slapping people?" That was a deal breaker (though not really).
He snickered at her suggestion, couldn't help it. "I do. I've a lovely pool, too, great for a dip between galaxies. But, no. It's been there, one of the older rooms, actually. I think." His brow wrinkled as he considered that a bit longer. Sometimes he lost track of what all was in the ship. "Just remembered where it was is all, dramatics! Love the flare! Must be why Shakespeare and I got on so well, hah!"
That was new. While his grin didn't waver, he did glance down for a moment. Was he doing it again? What he'd done with Martha and not even realized it until she was leaving him? Attempting to take it in stride, he opted for humor. "Oh, would have loved for you to meet my best mate. She'd be in stitches over this. No, that's quite all right, but I think that a bit of hand-holding is integral to a good run, not to mention making it across the universe and back again. Your loss!" He ended in the most lighthearted of fashions before breaking into run.
"Allons-y, Sam!"
He'd show her the medical bay, the lab, most anything she wanted before making it back to control to resume repairs. Best to get her familiarized with the bigger picture before concentrating on the lesser (but no less important) pieces, ever the methodical madman in a big blue box.