I can recommend the VR City Hotel. We stayed there Jan 2020 (pre cruise) in a twin room. It is 3 star but was modern and comfortable with friendly staff. Our room also included, IIRC, fridge and washer/dryer. It is close - walking distance - to CBD, many cafes and restaurants, and about 10-15 min walk to the waterfront precinct. There is secure parking available AUD30 p/d.
Possibly a drawback is that it is on a steepish hill but it was not a problem for us aged 68 and 70 at the time but if you're young(er) and in good health it should not be a problem.
https://vrhotels.co.nz/vr-auckland-city/location/
You have a choice of many in your price range so you may need to spend a little time researching with a Google map of the area and I'd suggest checking out reviews on Trip Advisor.
https://www.tripadvisor.com.au/Hotel_Review-g255106-d601522-Reviews-VR_Auckland_City-Auckland_Central_North_Island.html