A/N (2017):
I discovered this in the depths of my tablet, from 2014, and decided I might as well post it here. Apologies for past-me's writing.

A/N:
My retaliation to an excess of TenRose (thanks, sis). Shameless Rose-bashing. Sorry-not-sorry.
Inspired by Moffat: "You have to hand it to the Doctor for dumping a slightly needy girlfriend by palming her off on a copy of himself. He tried leaving her in a parallel universe, and that didn't work."
In other words, another way the 10th Doctor could've got rid of Rose.

Obviously, some of the characters are OOC.

Disclaimer: Doctor Who and PJO aren't mine. Unfortunately… The rights must have got lost in the post (like the Harry Potter ones).

Step 1: Land in Camp Half Blood

Rose had been pestering him to go off camping for ages. This morning was no exception:

The Doctor stumbled into the kitchen of the TARDIS and began to make himself a cup of heavily-caffeinated tea (racing around the Lambda-Hyperion system with no shoes all night had taken its toll, but he'd needed some alone time). The girl in question was already sitting at the table with a bowl of cereal.

When she noticed him, she began her chattering 'Doctor, you've promised we could go camping six times now.' Had he? Damnit. '… and we never have. Please? I just want some normal non-alien countryside for a change? You can pick the year an' all. You see, when I was in Year 10* we did our DofE* and went camping in – Dorking*, I think it was? – and it was great fun. Me and my mate Shareen, we- ' Normally her mindless chatter would've washed over him but today it was grating.

'Of course. Why don't we go for near future? America sound good? I know this great spot in Yellowstone Park, beautiful views. Virginia Woolf and I once got caught up with some Axons there, but afterwards we ended up camping and it was brilliant. You know…' The Doctor went in at the right moment and played his part of enthusiastic alien friend (or was it more than friend? By the number of times they'd kissed it probably was, he realised) like he always did, although his hearts weren't in it.

An hour or two later Rose had finally dressed and they were in the console room. The Doctor flicked a couple of switches, pressed a few buttons and pulled a few levers and gave a final wiggle of the zigzag plotter (not strictly necessary, but a nice flourish) and the TARDIS started to rasp its way through time and space.

Soon enough they materialised on a hill. Eagerly, dragging a massive rucksack (presumably full of tent) Rose dashed out. The Doctor followed, and breathed an inward sigh of relief – they'd arrived exactly where he'd intended.

Rose turned to him in confusion, indicating the mass of Greek-style buildings below them. 'Doctor, where are we? I've never exactly been there, but I know enough to know that this isn't Yellowstone.'

In his usual charade, he inhaled deeply and answered immediately 'Friday 28th August 2011, two minutes past three in the afternoon… Somewhere in the New York, probably Long Island. This seems familiar for some reason.' Of course it did – he had visited Camp Half Blood frequently over the past few hundred years.

Landing here was all part of his (OK, hasty but still very clever with lots of backups) plan to get rid of Rose - it didn't have to be permanent, necessarily, but a break at least was necessary for him to maintain his sanity.

It was twelve minutes later that they were first spotted (twelve minutes filled with whining, three attempted kisses – and one successful one – and incessant complaints from his companion as well as an impossibly fast explanation from him. Honestly, humans were so slow sometimes.), by a tanned and athletic teenager of around 16, with a shock of black hair and sea-green eyes. The Doctor presumed this was the famous Percy Jackson that Chiron had gone on about last time they met.

'How did you get in?' he asked shortly, almost menacingly. The Doctor noted that his hand went almost instinctively to his right pocket, where a suspiciously normal pen was sitting. A quick scan confirmed that it was unnaturally high in deitic energy (what the demigods would probably call magic) – it probably turned into something weapon-y. Maybe a sword. The demigods were known for their violent methods, after all.

'We were just walking along, our transport…. broke down over there.' supplied Rose, gesturing vaguely at the TARDIS.

'Not you,' the demigod said tersely. He pointed behind the pair. 'Them.'

The Doctor turned around and noticed about a dozen cyclopes about a hundred feet behind them.

'Oh.'

*9th Grade to all Americans out there.
DofE (Duke of Edinburgh award) is like this challenge that lots of teenagers do. A part of it is walking at least 24 km (about 15 miles) in 2 days and camping over night in the wild. I'm not sure if they have it over there?
Dorking is a place in Surrey (that's the county south of London) with lots of countryside.
I think that's all the cultural notes ;-)

A/N:
Thank you for reading, and do review. I'll probably post the next chunk every couple of days - if I remember.