Best farmstays scenery wise would be Central Otago - (Queenstowns - Wanaka area). 3 -3.5 hours drive from Dunedin.
Mid April there is great autumn colors around Arrowtown.
The Catlins, 1.5 - 2hrs south of Dunedin is a great spot for Waterfalls, Yellow eyed penguins, NZ Sealions and a petrified forest on the beach.