Notebook supporting TeX maths and code highlighting

I've had this problem for a while, a lot of people around me (sciences) seem to have this problem as well, and so far I haven't found a satisfactory solution.

I would like to find a tool for taking notes:

• which can synchronise notes reliably across devices (at least all *nix OSs supported);
• which supports maths in a LaTeX-like syntax, as well as code syntax highlighting, with a friendly syntax, and preferably in a Language that allows function/macro definitions (LaTeX is quite good, but I've never head anyone telling that TeX was an easy and intuitive language..);
• which can export a specific note as a standalone document (say PDF or offline html);
• preferably coming with an integrated UI;
• preferably free (but I'd be willing to pay for a good solution as well).

Of course, I could always setup a folder on Dropbox with a template LaTeX document and write my notes like this -- but call me lazy, I feel like writing a full-blown LaTeX document is not as simple as taking notes should be (even though it is my favourite choice when it comes to writing reports or papers), and even though a file-structure can be as tidy as you want, exploring it in the console or in a file explorer doesn't feel like you're going through your notes.

The closest I've seen is probably using strapdown. I find this library beautiful, but I feel like it's at the other extreme; although Markdown certainly feels great for short notes, when things start getting a bit longer certain features are really lacking, like the ability to create and reference (sub)figures with captions, automatic section indexing, equation numbering, etc. And as with an ad hoc LaTeX files solution, it's not integrated into one nice centralised tool. Same story with pandoc, though it does seem more capable.

Finally, integrated tools like OneNote or EverNote usually don't support both LaTeX formulas and code syntax highlighting. But they definitely provide the integrated experience that one could wish for taking notes, and allow to synchronise things across devices.

I know there is no right answer for this question, but I would be curious to know about what you use, and if you know a tool that would match the requirements I set out up there?