While I'm no game designer, I do personally feel Vayne is one of the best designed champions. All of her abilities fit her night hunter theme very well and they tie with each other very well while leaving a bit of room for user creativity (stealth jukes, dodging, great condemns, etc.). She has a higher than average skill ceiling but as CapWed said she also has a decent amount of 'pick up and play' to her. Largely I'll attribute that to Tumble. Most of the time new Vayne players will just use it for the aa buff, maybe a bit for dodging, then later as they get better they'll use it to set up condemns, do some awesome bush-play, and use the tumble ability itself to better use (when one realizes the CD doesn't start until an aa happens). Honestly, I feel she is both the best example and best introduction to a hyper-carry.
As for her place in the current meta, to me she doesn't feel as good as she used to but only because the same bit is for adc's in general. (Which, for the record I am fine with, while adc's should be able to 'carry' they shouldn't be able to single handedly win the game) She can still hold her own and still has that 'time-bomb' feel of a hyper-carry, but with all of the strong cc and damage supports going around (Braum, Thresh, Leona) she's not having the best of times in bot lane right now. She does better, imho, against squishier caster supports who aren't as readily able to shut down her early game. So the bot lane meta's working a bit against her but not horribly. (You can try Vayne top is you feel risky XD)
The only real complaint I can think of, and don't even mind it that much at that, is her passive. Love the effect and all, but it can get a little bit unintuitive when you think about what defines "going towards". If I recall correctly her passive is actually a 180 degree angle with a huge range for the enemy champion check. That, and it's one the last things I find new Vayne players noticing and using effectively as it's somewhat subtle until you ult. But, again, I don't mind it that much because even if you don't notice it you still use it whether you want to or not.
All in all, Vayne is one of my favorite adc, a major factor also being she was the one I got my very first Penta with (SR Penta, not murderbridge penta).