We have two sliding glass doors in our house. When we moved in a year ago we installed vertical blinds on one of them (the house was new construction so there were no window treatments when we moved in), but not on the one in the living room because, like you, I don't really like the look of vertical blinds. I wanted a softer, more stylish look for the living room, so I opted to do a double-curtain rod with some semi-sheer green curtains and a white sheer curtain liner behind. I think it looks nice, both inside and from the outside.
Let's see if I can find a picture or two...
This one is from outside and it's kind of far away, but you can sort of see the white curtain in the window:
Here you can see the curtains on the right side of the photo:
When the sun shines directly on that side of the house they don't block all of the light, but they do at least provide privacy: