Norfolk Island certainly fits the bill. And at less than two hours flying time from Auckland, even the trip is small.
Administered by Australia, but with its own distinctive history and a robustly independent attitude, Norfolk Island is the kind of place you can really escape the stresses of your everyday life. You can relax in lush scenery, explore the historic buildings, and finish off with a plunge into the crystal-clear Pacific waters that lap the island's many beaches.
Polynesians discovered and then mysteriously abandoned the island around the time Aotearoa was being settled. Next on the scene was Captain Cook, who noted the towering Norfolk Pines and described the island as 'paradise'. High praise indeed, from a seafarer who spent time in Tahiti, Hawaii and many other famously pretty places.
Don't come here expecting towering hotels and fast-paced nightlife. Instead, take the opportunity to unwind in nature and explore the local attractions. Swim and snorkel in Emily Bay, taste the wines at Two Chimneys Winery, and wander through some of the oldest Georgian buildings in the southern hemisphere. You can also try your hand at fishing – ask about the local charter boats.
If you're a history buff you'll know that Norfolk's first European residents were convicts, who turned up not long after the first fleet arrived in Sydney. The shackled loaf-stealers have long since departed but there's a reminder of their presence in historic buildings of the Kingston Arthurs Vale Historical Area (KAHVA).
At only eight kilometres by five kilometres, Norfolk is easy to travel around. There's no public transport and only one taxi. Bikes and cars are easy to hire, and you won't have to worry about airport transfers, as your accommodation will send a driver to pick you up and deliver you to their doorstep.