As long as you meet the general entry requirements for New Zealand (such as having a valid passport and meeting any visa requirements), and do not have any other serious criminal convictions or are considered to be a threat to public safety, you should be able to travel to New Zealand.
However, it is always a good idea to double-check with the New Zealand embassy or consulate in your country to make sure there are no specific restrictions or considerations for individuals with a DUI conviction planning to visit New Zealand. Be honest about your DUI conviction when filling out your visa application and be prepared to provide any additional information or documents that may be requested.