The Wellington Botanic Gardens lie on the southeast side of the valley that runs up to the suburb of Kelburn. From downtown, take the cable car from Lampton Quay. Or walk up Glenmore Street towards Kelburn.
The gardens are a modest walk in distance, but some sections of the hill are steep. At the top of the hill, near the cable car, are some gorgeous mature redwoods, followed by some native bush and fernery.
Walking towards Glenmore Street, you will see a series of lovely gardens with native and exotic plants. The Treehouse is also worth a visit, with nice views over the valley. Continuing from the bottom of the hill northeast, you will see a large rose garden, the Peace Flame, and a cafe.
Across the road from the Glenmore Street entrance is a track entrance to Te Ahumairangi (Tinakori Hill) off Kilmister Street. This is a large town belt area of mostly bush on the side of a typically steep Wellington hill, with more amazing views.
