One of the trappings of being in a big city like Auckland is that you'll never be far from the nightlife; unless you've wandered into an old-money neighborhood packed with villas and manicured lawns where the owners (naturally) drink single-malt scotch and have fully stocked wet-bars on each floor. If that is the case, either retrace your steps to the city center or knock on the nearest door. The worst you can be told is no.
Apparently we've veered away from a general take on the city's nightlife into the hypothetical moral quagmire of inviting yourself into the homes of wealthy folks in an effort to drink their alcohol. Let us correct the course before we get any further.
Auckland has the full complement of nightlife options. From glitzy cocktail bars to classic Irish pubs to bass thumping dance clubs to craft beer joints, there is an establishment for any and all tastes. For those that follow the usual tourist paths, the Viaduct is a safe, expensive option for both drinking and dining of the slightly more expensive variety due to its enviable views over the Hauraki Gulf. Just across the water is the suburb of Devonport, which has a quality string of restaurants and bars along Victoria Road, but this also comes up frequently on the usual tourist radar. If you don't mind, you've got a few (again, somewhat expensive) upmarket bars here that'll be calling your name.
Although you'll find a scattering of music venues, clubs, bars, and lounges scattering all over the CBD, Ponsonby Road, Karangahape Road, and the Queen Street/Vulcan Lane area are the most considerable concentrations of nightlife. Ponsonby takes the cake for its inviting, upscale, artsy vibes, and has a number of packed bars and clubs come the weekend. Karangahape, or "K Road" as the locals call it, is often sold to travelers as as quirky Auckland, but it's undoubtedly one of the more seedy areas of the city. Which isn't to say that there aren't a few establishments that rise above the reputation (Hard Luck Cafe, underground bands at Wine Cellar, alternative stand-out Coco's Cantina), but it's a neighborhood that can be off-putting for those who expect everything to have that rosy New Zealand sheen. Queen Street/Vulcan Lane to the north may just be your best option if you're into craft beer specialists (Occidental, Vultures Lane, Fort Street Union, Bluestone Room), while there is a good range of outlets for other tastes.
If you're looking to get out, Mission Bay to the east has great views of Rangitoto from its promenade, as well as a dozen or so drinking locations. For more on what's available for your nights out in Auckland, take a look through the included links and activities.