I'm doing my BEng from the University of Auckland (I assume that's the uni you plan to attend?)
I have lived in Auckland almost my whole life, so I can't give a solid comparison to Pakistan, however, I definitely recommend coming to Auckland. The quality of education is great, you won't get a much better quality of life anywhere outside of New Zealand, and it is a great place to settle down, a lot of potential here.
I personally live with my parents, however I have a lot of friends living alone, and you are absolutely correct in saying that Auckland is one of the most expensive cities to live. The university lodging and anything else in the CBD are extremely convenient for students, but will most likely be too expensive, the majority of my friends who live alone do flatting in one of the central suburbs around the CBD, or a little further away if the public transport connection works out. Bear in mind that driving to uni is not feasable at all, so public transport connection should be a big factor in deciding where you stay. Even though Auckland is expensive, in my opinion the amount of money you spend to live here is absolutely worth it, especially if you plan on settling down here.
There are a lot of clubs you can join at uni (and outside) uni, including things like cricket, hiking, gaming, etc. Auckland is great for recration, especially in summer. There are great beaches all around Auckland, awesome hikes, and a lot of parks and reserves. NZ is a fairly small country, so the main tourist destinations are not out of reach other. Some big North Island attractions such as Rotorua, Coromandel Peninsulia, Tongariro, and Bay of Islands are within 2-4 hours from Auckland. Halal food is also very readily available due to the fact that NZ exports to the Middle East, and therefore the majority of places serve meat that is halal even if they are not certified. Regarding nightlife, I am not really an expert on this because I don't really party, but nightlife is mainly in the CBD, where there are a few clubs, and there are also parties organized by university clubs/student bodies. Auckland Uni is not really all that known for it's nightlife/party life, The University of Otago (in Dunedin) is considered to by NZ's party university.
There are modest amount of Pakistani students in Auckland too. I strongly recommend you join Pakistan Facebook groups such as Pakistanis in Auckland, Pakistanis in New Zealand, Pakistani Students in New Zealand as they are often helpful for new people here, and you often get good arrangements for flatting, buying cars, etc on there.
Feel free to ask anything else