She strikes a lot of rare balances that few other characters really do in fiction. I'm not sure how much of it is just me projecting, but from my pages upon pages of writing I assume many anons feel the same way. She is a very motherly figure, and exudes gentleness and nurturing wisdom in her disposition. That's not very uncommon. But she's also a bit of a misanthropist at the same time, and is very, very solitary even by Touhou standards - a cast already full of introverts. These are two core personality traits that don't often exist simultaneously within a single character, and it makes Yuuka extremely interesting. She's at once a beautiful mature woman, who dresses modestly, carries a parasol and partakes in delicate hobbies such as gardening, sipping tea and sleeping indulgently. But at the same time, she purposefully enjoys picking fights with people, teasing, and - as ZUN described - it's very hard to know what she's actually thinking.
It's easy to think she's just a callous individual who enjoys the reflection in her own mirror and the sound of her own voice above all else, but I don't think that's the case either. Her music in lotus land story/pofv is absolutely beautiful and full of nothing but raw passion. Arguably some of the more intense pieces ZUN has ever composed. I sense a lot of longing in a song like Lotus Love, and it's really intriguing. Somewhere along the line, I came to the conclusion that she is a woman who wants genuine love more than anything else, but simply has more love than any man would ever be willing to accept. So she hides behind a mask of indifference, her true emotions too powerful to ever see the light of day. I see her way of speaking as being somewhat of a test - to see if anyone has the patience, the perceptiveness, and the sensitivity to keep up with her. Most people are quite lacking and when you're someone of Yuuka's caliber, you'd see that easily. This sort of "problem" she has is deeply relatable to me. I at once despise people (basically everyone I know) but at the same time I am quite a passionate person and I obsess over beauty and aesthetics constantly.
On the same note, she is extremely beautiful. Messy, wavy hair, the contrast of green with deep red eyes, a simple but charming outfit. Both her PC98 and Windows designs are amazing. As are the fights in said games themselves, absolutely dazzling and one of the best examples of Touhou's style of danmaku as an art form.