Would you be happy with non-1980s full tiled walls?
Radiator position looks slightly odd, I'd probably want that moved too like pp says I'd possible. You may already be aware, but if you replace a normal radiator with a heated towel rail you need to get one that's double the size of the previous radiator in order to still heat the space effectively. Can't remember if it's just double the height or double the width too - possibly only height.
You probably would be fine with half tiled on the wall with sink as long as they came up high enough (maybe a bit higher than strictly half). You could also extend them higher over sink but may look odd in middle of wall, so I'd probs go for two thirds or whatever height along whole wall to be enough for sink splashing up.
If I could afford full tiling, and there were tiles I liked enough, I might go with full tiled walls with your layout even tho I'm not normally that keen.
I wouldn't want horrible white glossy tiles like in a hospital or office or train station, but there are some lovely neutral wall tiles about that look great without the major dating problems of patterns or fashion colours.
You don't necessarily need to have the same tiling on all four walls either. Whether that's a single wall with different tiles or one pair of adjoining walls with slightly different tiles to the other pair (so 2 L-shapes on aerial plan).
Our current bathroom (which is small rectangle too) has an L-shape of 2 full tiled walls, and then the other L-shape of the other 2 walls are two-thirds tiles with slightly different but complementary tiles. I think in a small space it makes it feel less samey / like the walls/tiles are closing in on you!
It's a bit sad but I genuinely love our bathroom wall tiles. 
If you look at home interior and tiling brochures you'll probably be able to find well-executed examples of what I mean.