Catherine the panel blinds could be your solution. They are available in sheers, patterned, mixed etc and operate on a track system. It's an update of the verticals that a lot of homes have. If you have Ikea in NZ you could sus them out there.

I'd match the white of the door trim and baseboards.

I agree with Diane's ideas! Grey is a nice color. The only thought I had on having a corner sink cabinet, you may not be happy with it in the end. You have a little corner, and the sink may be too small for you in the end along with not having any storage space. If you can't find any curtains that you love, try a cheap roller blind for now. It will give you a visual look and an idea if you want to stay with a curtain or going a bit modern with a patterned blind or even a roman type shade. It could turn the cozy look into a clean modern look. Framed mirrors are expensive. Call a glass company in your area and have them give you a price on mirrors. It might be quite nice to take the mirror down, and replace the wall there with a complete wall mirror to fit, stopping the mirror at the vanity, and continuing the mirror across the vanity between the sink and window. It will make your bathroom feel much bigger, even though you wont be able to see in the mirror over the sink. Close up the vanity doors with new door. Use props first (white poster to cover up the doors) etc. before you buy anything! Stick on tiles are a great idea! They clean nicely and look great. Although I wouldn't go with the wood look. Your bathtub tiles are old fashioned, go with a stick on floor tile that is easy to look at, try to get samples first. Remember Gray is a sleek clean modern color. It is not a cozy country color. If you don't like the grey in the end, maybe a real pale blue or butter yellow (that would be more of the cozy cottage look).

I would clean up first. Especially the stuff growing in the paving. Then get gardening with pot plants and start experimenting with different plants and the positions. See what you like and if you can keep it alive! Our house has the sun setting over the back fence and we've done a few inexpensive things to reduce that issue (most expensive were outdoor blinds around the verandah) but for most of the year we just don't want to be out there. It is hard work to keep the plants going in summer, there is a lot of sand due to the difficulty in keeping lawn alive and it is just bloody hot. So, that's why I'm saying clean up, start gardening small and see how you go before committing to structures that might not address the real issues you have with the yard. Just my 2 cents! :)