Given I'm the closest to this I should pipe up. Queenstown has had a tough time the last two years with our very strict border rules - which should hopefully subside so that we can welcome visitors next kiwi summer.
Arrowtown is as Tom has described it. Super cool place. My personal favourite generally aligning with my values (although sometimes rather soft from overwatering). The high season visitor rate is NZD$140 which is US$93. For locals it is a very affordable membership with cheap members guest fees + members have all kinds of rights to play other courses in the region.
The Hills is indeed on big rolling land. The original routing is a bit clunky but there's some cool stuff there. Darius Oliver has built a 9 hole par three course called The Farm which is bunkerless and oodles of fun. For most people on this site, rolling around the Farm in the evening with 2-3 clubs would be a hard experience that is hard to beat in NZ. The team at the Hills have also made various design changes to the main course working alongside Darius. These include widening fairways, removing bunkers and providing more options from the tee. With the climate (and a prior commitment to annually hosting the NZ Open) there have been limits on the amount of change that can be done. Some holes play significantly differently like 9, 15 and 18 with large bunkers removed from the fairways. Whilst The Hills has hosted many tournaments it is no longer the host of the New Zealand Open. I've spent a lot of time at The Hills over the last 10 years but at this time it is no longer the host or co-host of this event. The Hills were fortunate to have an excellent GM/Superintendent who made huge improvements to the golf: building The Farm, changing mowing lines, minor strategic changes and crucially putting the members through a fair amount of short term pain to improve the turf quality which is now world class. He is now involved in a new project in the North Island. Like many courses discussed on here The Hills is private (which is an unusual phenomenon in New Zealand). Before the pandemic they allowed very limited guest play for NZD$1,000 which included F&B. I'm unsure what their plan is moving forward with regard to guest play but like most private clubs it's a peripheral part of their business model.
Millbrook Resort was the original 'golf resort' in Queenstown. Originally it had an 18 hole course designed by Sir Bob Charles. Now it has two 18 hole courses - the final 9 holes opened to visitor play January 2022. The new course is designed by Greg Turner & Scott Macpherson and is called the Coronet course. Over the years Turner & Macpherson also made various changes to the original course (including 4 new holes). Millbrook Resort is a very successful golf lifestyle resort & I can't think of a better place to stay when visiting the area. They are now the hosts of the New Zealand Open with the pro-am style event (format is like the AT&T) played across both courses. Unfortunately the event has been cancelled the last 2 years (this week the 2022 event was cancelled). The resort is at it's finest during the tournament where thousands of people stay across the 400+ residences & in the hotel - many of the amateur players are international, a number are from Japan (Millbrook Resort is owned by a Japanese family) and a few are playing this week in Monterey. Architecturally there are always limitations within the residential constraints but the Coronet course with a continuity of style features width, strategic options (particularly on the par fives which are excellent) and plenty of fun shots. I suspect as more people see this course it will be considered amongst the top 8-12 courses across the overall NZ golf offering. High season non guest visitor rates are between $210 (USD$140) and $260 (USD$172) with various discounts for hotel guests and replay rates.
Jack's Point is almost certainly the most stunning golf course in the district. It has been designed by John Darby. Some commentators rate it extremely highly and it has some incredible moments both architecturally & visually. This is supported by absolutely impeccable conditioning with firm tight fairways that merge into natural areas. I have difficulty with the routing and a few other things but the reality is that for the average punter riding a golf cart who isn't into architecture this is the number 1 course to recommend in the area (comfortably above Arrowtown). Even most architecture snobs would have a great time out. Fees are NZD$195 (USD$130) and a replay rate of $95 (USD$65).
There is a private course above Arrowtown owned by Russell Coutts. It's got 16 greens, shared fairways and is very very cool. You chart your own path around the property to greens that have a lot more undulation & interest than others in the district. Probably shouldn't mention it on here as it's essentially his backyard!
And finally there is a new course that has been consented immediately next to The Hills and across the road from Arrowtown. It's called Hogan's Gully. The landforms are a mixture between The Hills and Arrowtown. I've walked the routing which has some stunning moments & it will definitely be one of the most exciting golf courses to come online in New Zealand over the next few years.
Finally, Queenstown (and surrounds) is about a lot more than golf. I'm biased as I now live down here in the South amongst the mountains, the lakes and the big skies and am very lucky to call this special corner of the world home.