In a word, no. Nestled between rolling hills and an expansive coastline, New Zealand's capital city is compact enough that your two legs will get you around most of the key attractions.
And, should you wish to venture across town to, say the stunning natural sanctuary, Zelandia, one of Wellington's cheap and efficient public buses will get you there from the centre of town in about 15 minutes.
If, however, you wish to venture further from the city — such as over the winding hills to the glorious Wairarapa wine region or even to sample the vintage shopping delights of Petone, the Dowse Gallery in Lower Hutt or the Kapiti Coast's beaches — then renting a car is easy. All the main global hire car companies are represented here and there are also a variety of privately owned car rental agencies. The internet is your friend in this instance.