Mount the crossover inside the door, but slip it into a taped-up plastic bag to keep water off it. They don't need to be on display, and IMO they look crap when they're just screwed onto the door card.
Try a few different mounting positions for the tweeter, like down with the woofer in the door, up the top of the door, on your kick panel, on your dash, etc. Choose the position that sounds best to you.