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I would go with a peri blooded aasimar mindchemist alchemist with the eldritch heritage feats (Maestro bloodline), and the Master Craftsman feat with Craft: Gadget and Craft Wondrous Item. As others have said before, the TARDIS would be an artifact all on its own.
Peri blooded aasimar: Dualistic nature, good with a hint of darkness, he's an outsider, both literally and figuratively. If your DM will allow it, you could trade out the SLA: Pyrotechnics for another +2 int, for +4 int, +2 cha racial mods.
Mindchemist Alchemist: You trade out mutagens for cognatogens, which bump mental stats instead of physical stats. Also, at 2nd level, you get an ability called Perfect Recall, which lets you double your int bonus to knowledge checks, as well as Int checks to remember something. Furthermore, the alchemy stuff can be completely justified as non-magic, which also fits his theme.
Eldritch Heritage (Maestro bloodline) feat chain, coupled with Perform (Oratory): The newer Doctors (especially David Tennant) love to talk a million words a minute. The first ability of the feat chain lets you talk your enemies into a Daze. The second ability of the feat chain lets you Fascinate your enemies as you talk circles around them. The third ability makes it so that you understand and can communicate with any creature able to understand language.
Craft: Gadget with Master Craftsman & Craft Wondrous Item: Ability to make a mechanical wondrous item, a la Sonic Screwdriver. I'd think abilities like Knock, various Detect spells, and perhaps some protections would cover the spectrum.
That's my take on the Doctor, at least.
I've had success with Lore Oracle with Tongues curse (technobabble during combat). Lore Keeper and Focused Trance revelations to succeed the really hard knowledge checks (put at least a rank in every knowledge skill) Cha-times-per-day, which would be useful in PFS mission/faction objectives. Sidestep Secret is basically act as "plot-armor", so you can focus on Str and Cha. The bonus spells are decent for figuring out or finding magic items or treasure; tongues as a level 2 spell has been great for me to understand languages or simply give party members the ability to know what's being said too.
If this wasn't a PFS game but a long-term home-game instead, Aasimar favored class benefit with Mental Acuity revelation would mean Int would be advanced really quickly.
off the top of my head, i'd say an archaeologist bard. grab the Run feat. know everything about everything, and good enough at any task to get the job done.
EDIT: dunno why id suggest taking the rogue talent for prestidigitation when its a class spell. im dumb i guess.
or simple wizard could also suffice--have his bonded object be a wand (the sonic screwdriver, naturally), grab the run feat, invest in a wagon and have it spelled for more room on the inside and various lab tools, books, etc. keeps some scrolls of comprehend languages on-hand (or have your wand be one of comprehend languages), and various minor spells can cover lots of the things he does.
the doctor reminds me of gandalf a bit--he's got this huge reputation for being awesome/powerful, but really he just thinks quickly and does lots of minor things that help out in the long run.
I second the Alchemist. There are many variants to choose your Doctor from and the 'wackiness' comes along with the class.
Mind Chemist would fit, but also the Internal and even Grenadier with the alchemical weapons ability seems to have something there too.
As far as race, Aasimar does seem to fit best.
it does seem like a fun build type as I've always have been a fan of the Doctor's 'non-combatant' solutions to problems.
Have fun and please post what you went with.
I have been wrestling for about a year and a half now about how to best approximate The Doctor and even Gandalf in a Pathfinder game. In the end, I think those two characters are more similar than dissimilar; they come from nowhere and save the day with their superior thinking and insight, rather than brute force (usually).
That being said, the way to 'properly' build The Doctor is to build the strongest possible character, that you *play* mercifully and almost like a pacifist. And yet, he is utterly fearless and will stand up to anyone and anything. He faced the Parasite God in the Rings of Akhaten, he even confronted the Devil himself without hesitating. He fought on the front lines and he's the sole survivor of the Time War for a reason.
Remember this bit of context:
"He's like fire and ice and rage. He's like the night and the storm in the heart of the sun. He's ancient and forever. He burns at the center of time and can see the turn of the universe. and... he's wonderful."
And,
"He never raised his voice. That was the worst thing... the fury of the Time Lord... and then we discovered why. Why this Doctor, who had fought with gods and demons, why he had run away from us and hidden. He was being kind..."
That's not a description of a Bard...unless he's got 10 Mythic tiers. The Doctor (and with a slightly different build, Gandalf) are both God Wizards, or possibly Mystic Theurge/Arcane Hierophants. They hold back because they are trying to give you a chance to survive. ;)
There's no way to really build the Doctor, I agree. Interesting challenge, though. I think you'd definitely have to take enough levels in reincarnating druid until you get the reincarnation power. Then probably the rest in archeologist bard (or at least one level to get all the knowledge skills as class skills), then maybe witch as suggested earlier. Or sorceror. The new Doctors all are focused on a massive charisma. He would have bluff and intimidate maxed as well as knowledge. Have to have use magic device and craft wondrous item, too.
Or you could just stick with the reincarnation druid and call his animal companion his companion and just swap it out for something different every couple of levels (the Doctor isn't one to keep his pets around for too long).
I also think he'd really rely a lot on a wand and have the staff-like-wand feat. Probably craft wand, too.
Samsaran Rogue / Oracle (of Time) multi-classed character. His oracle curse would be "Tongues", in which he speaks in riddles and far-flung, future math/science lingo. His screwdriver could be constructed as a staff (though shaped like a wand), for which he has plenty of ranks in Use Magic Device. His companion(s) could be represented by the Leadership feat, of course.
Time oracle with the legalistic curse. All I have to say is in defense of legalistic's penalty is "I can't interfere in this it is a fixed point in time" and to it's boon "I call upon the 8th accord of the shadow proclamation, you are to lay your weapons low or face the consequences!"
Ooh, I hadn't thought about that. Fits really well! Perhaps he's got the "Dual-Cursed" archetype (with "Tongues" serving as his secondary curse; techno-babble, as has been previously mentioned).
It's decided--I'm playing this character now! I want to see how long it takes my fellow players, especially my girlfriend (with whom I've regularly watched the show), to catch on... just gotta wait until the next campaign starts up (that I'm not running, of course). Damn... who knows when that'll be.
With the Extra Traits feat, he has 4 feats to work with. Grab a drawback and that makes 5.
Traits:
- Adopted, Human (Due to his time spent among the younger race; he's picked up a lot of their traits, or perhaps, because he sees a lot of himself in their actions; grab "World Traveler" as a race trait.)
- Grief-Filled (Due to the loss of his people and the many mistakes he's made in the past.)
- Mathematical Prodigy (Due to the fact that... well, he's the Doctor!)
- Patient Optimist (Due to the fact that he keeps trying; he's also willing to give many villains a second chance, except when he's the 10th... he's a bit grumpy.)
- Witty Repartee (Due to his frequent banter and the well known fact that the Doctor lies.)
- World Traveler (Due to the fact that he's literally a world traveler.)
Drawback:
- Sentimental (Due to his incredibly long life and the fact that he's seemingly absent-minded enough to run into trouble every episode.)
Edit: Ahhh! "Adopted" is a social trait, meaning he can't also have "Grief-Filled"! That won't due at all... would have to convince the DM that samsarans are close enough to humans that he can select "World Traveler" as a race trait. That, or well, just make him human and drop "Adopted".