I reall like the current colors and your red roof. I think you can change the house colors and not change the fence color. Here is one example that is in a tan family: With a white trim and dark brown shutters, I think it would work. Here is another example of a tan shade: I also like this light grey with white trim: Would you consider a green base: Then chose either a brown or red for the shutter.

I like @kelly's idea of picking a lovely fresh color of paint for the door. You can then bring it down onto the stair risers. Either a solid color to match the front door, or go wild and add some decorative elements to the risers with stencils. Or think of staining the door a great color and coordinate the stair railings and risers. I have an idea book put together for just such project that might spark some ideas for you. http://www.houzz.com/ideabooks/16700983/thumbs/Kathryn-Delany-s-Decorative-Stair-Risers

All the suggestions above are perfectly good. However, when you have a house that is entirely painted, the options are so endless that it's easy to get stuck. I'd advise either finding photos of comparable homes in colors that you really love, and reproducing a similar palette on your home… or upload a picture of your house to a colorizing site, and play around with various combos. Sherwin Williams has a Color Visualizer that is decent. I don't mind a white house, but feel that the black trim is a bit harsh. On the railing especially- it feels like it is outlining itself too much. Reduce the contrast between the body and the rail and it will enhance the house rather than overwhelm it. You have a lot of choices, so just experiment and go with what resonates with you.

I don't know how hot it gets in Auckland in summer (I've only ever been to NZ in winter!) but if it gets hot, then go for a pale colour. Dark roofs should be kept for cold places!