@contrex,
I just 'tested' myself and intuitively I say/think and use:
bring (with) (to)
take (from)
In other words, I wouldn't say, 'I'm going to take a cake to her party.'
I'd say, 'I'm going to bring a cake to her party.'
And I wouldn't say, 'Don't forget to bring that book with you when you leave.'
I'd say, 'Don't forget to take that book with you when you leave.'
But in terms of going to an actual place, I find that I use take instead of bring, almost exclusively.
In other words, I'd say, 'I'm taking her to the airport tomorrow,' unless, as McTag said, I'm going anyway and she's coming with me. Then I would say, 'I'm bringing her to the airport with me tomorrow.'
But I do think it's just a matter of personal choice - the difference is so subtle that I don't think either could be classified as right or wrong.