Not far from Wanaka, on the NW side of Lake Wanaka, is Roys Peak. There is a big parking lot at the start, and it's marked as Roys Peak Track.
It's about 8 km long, and about 1250 m Elevetation. And if you continue to Mount Alpha, it's another 3 km and 280 m elevation. You could continue on the ridge to Cardrona Valley Road, but then you have to see, how to get back to your car.
I just went to Mount Alpha, and then back.
The path to Roys Peak is like a highway. The Mount Alpha Track is a narrow path, but quite clear.