Wellington is the terminus for InterCity coach services to Auckland, Gisborne, Napier, New Plymouth, Tauranga and Wanganui/Whanganui and there are direct coach services to destinations throughout the North Island including Auckland, Gisborne, Hamilton, Hastings, Napier, New Plymouth, Palmerston North, Rotorua, Taupo, Tauranga and Wanganui/Whanganui.
The Wellington InterCity coach stop is adjacent to platform 9 at Wellington railway station, which means that you have access to all station facilities while waiting for your coach including a good (but relatively expensive) New World supermarket.