Queenstown Gardens is just a short walk from the town center. Because New Zealand is safe, this makes an excellent romantic spot to walk around even at night.
This small peninsula offers a great view of the town and Lake Wakatipu while being on a small beach. Just a short walk to the other side of the peninsula offers a view of the Remarkables. This is fantastic sight at sunrise. There's also not many people there, so it heightens the romance.