Brian Burton and his wife should not miss my home town of Oxford, which is a quick rail trip from Paddington Station. A must-do is a walking tour of the colleges - this can be pre-booked and completed in a morning - followed by lunch in one of the historic hotels like the Mitre (or even in a basic cafe in the covered market).
The afternoon could be devoted to the museums - either or both of the Ashmolean and Pitt Rivers. Whatever they decide to do, Oxford should not be missed.
A couple of ideas for Brian Burton, but firstly a bit of advice applicable for all trips. Check the fares for the destination you are interested in on the British Rail website, as you will find they change for different times of the day and different dates. You can select the day's "Best Buy". Also, buy before you go as costs are much higher the closer to the time you travel, and it will be busy at the time of year you're going.
Bath is an easy day trip, with a variety of things to see, and has the advantage of having a hop-on, hop-off bus to get around the city (which in turn offers future discounts on similar buses in other cities). Don't miss lunch or afternoon tea at Sally Lunn's Historic Eating House & Museum, which also has an excellent gift shop in the basement.
Do not, like every other Kiwi visitor, ask the lady why their sally lunns don't have icing. The true sally lunn is quite different from the one New Zealanders call a sally lunn, and is served with both sweet and savoury accompaniment.
Winchester is another fascinating destination, much smaller than Bath, which makes it easily walkable. The Great Hall and the Round Table are near the railway station, slightly above the town centre, so make sure that you go there first, before walking down to the ancient cathedral and picturesque town.
They have a famous Christmas market, which will be a bonus while you are there - check which days it is on. York and Chester are two other lovely spots for New Zealanders craving history. Enjoy.
Fiona Downes, Castor Bay
Hampton Court Palace is a very short distance by train or boat along the river Thames. Strike the right time of year and they have a fabulous flower show and a magnificent music festival. The grounds are glorious and it is a lovely day out.
Windsor and Eton are a short train journey away too. The castle rooms are well worth the entrance fee, there plenty of little shops and eateries and a stroll across the river will bring you to the famous Eton school.There is some pleasant walking to be had along the riverbank too.
Chatham, to the east of London towards the Kentish coast, is a short train ride. It was a favoured place of Henry VIII and author Charles Dickens.
You'll find an ancient ruined castle, the river Medway, lots of shops and eateries including a traditional tea house, and Hever Castle, the childhood home of Anne Boleyn. The castle is a short walk through country lanes from the station. It has glorious grounds.
For lovers of gardens, visit Sissinghurst Castle, easily accessible by train from London. A bus meets the train at the nearby village and drops you at the front entrance to the gardens, and takes you back to the station again later in the day. The white garden is particularly wonderful. Hope this helps.