If you have a fair idea of where you’ll want to live in London, then try to find accommodations in that area of town. Or, you could stay more centrally, say in Westminster or Kensington and Chelsea, where there are numerous hotels to choose from. You can then use the Underground, a train, or a bus to get to the area of town that you want to explore. If you are unsure where you want to live, I suggest that you stay centrally. When you explore an area, you should plan to spend at least a few hours there. Use your time to wander down the high street, stop for a coffee or lunch—even find the nearest supermarket and see what it is like. You should also walk around the residential streets to see what type of accommodation is available.
You will probably be exhausted after your flight to London, so take it fairly easy on the first day. Once you’re settled into your hotel and refreshed, try a bit of easy sightseeing, perhaps by taking one of the tour buses that let you get on and off, so you can explore London at your own pace. You may also want to take the opportunity to wander around the area near your hotel to help you get your bearings, and explore nearby attractions.
The next day you should get down to business and visit possible living locations. I would start centrally and cover a few areas in Westminster, such as Mayfair (nearest Underground station is Green Park) or Belgravia (nearest Underground station is Hyde Park Corner), if you want upmarket, urban living. These areas border each other and so can easily be merged together in a visit. This area is near Buckingham Palace, so if you want to see the Changing of the Guard be there by 11:15 a.m. Another very central location is Marylebone (nearest Underground station is Baker Street), and you may want to spend some time here.
Families may prefer the quieter residential areas of St. John’s Wood (St. John’s Wood Tube station) or Maida Vale (Warwick Avenue or Maida Vale station), which border each other. The American School in London is based in St. John’s Wood, so this would be an ideal time to visit the school (be sure to pre-book a visit).
The next day you could combine a bit of sightseeing and location scouting, by visiting the parts of Kensington and Chelsea nearest South Kensington Tube station, followed by a trip to one or more of the South Kensington museums. If you think Chelsea may be to your liking, start at South Kensington Tube station and walk down Pelham Street and Sloane Avenue until you get to Kings Road, or you can take the number 49 bus. Once you are finished exploring this area of Chelsea, head back on the 49 bus to South Kensington, where you can visit the Natural History Museum, the Science Museum, or Victoria and Albert Museum (or all three if you are a museum buff).
The next day give yourself a break from location hunting and just enjoy London. If you like walking you could go to Parliament Square (Westminster Tube station). Here you’ll find the Houses of Parliament, including the bell tower that holds Big Ben, as well as Westminster Abbey. Then walk across Westminster Bridge and take a trip on the London Eye (you can pre-book online). Next you can walk up the river’s edge along the South Bank to The Globe Theatre and take in a play, or continue on until the Tate Modern. If you still have energy you can walk across the Millennium Bridge and up to Queen Victoria Street, where you turn right to get to Mansion House Tube station and hop on the Circle or District line to Tower Bridge to see the Tower of London. If you are tired, you can leave this to another day.
If you’d prefer a predominantly residential area near a large park, check out Hampstead, Belsize Park, or Highgate on the Northern line on your fourth day in London. Hampstead (in the borough of Camden) is packed with good independent schools, so build any Hampstead school visits into this day. You could then take the Northern line down to Tottenham Court Road to visit the British Museum and explore Bloomsbury. One last area I’d suggest that you visit would be around High Street Kensington and Notting Hill. Both neighborhoods offer a good mix of different accommodations in a fairly central location, but aren’t as busy as some of the central areas of Westminster. If you are going to be based in the City of London for work and want a short commute, then spend some time exploring around Islington (by Angel Tube station) or the City itself—this would be another time you could see the Tower of London, if you haven’t had a chance to yet. Even Canary Wharf in Docklands (on the Docklands Light Railway or Jubilee Underground line) could be worth a visit if you are going to be based there. If you are a tennis fan, then a trip to Wimbledon to do a tour of the grounds may be in the cards; just be sure to pre-book your tour. While there, you could explore the streets toward Wimbledon Common to see if it may work for you as a place to live. On the way back you could take the train to Clapham Junction and walk around Battersea and Northcote Road or take the District line train and get off in East Putney to quickly check out this neighborhood.
If suburbia calls, head south of the river to the borough of Richmond, by taking the District line to Kew Gardens (at the station, follow the signs to Kew Gardens and then walk down Lichfield Road to get to the gardens themselves). Afterwards you can go into Richmond and have a wander around its pretty town center before heading to the river and taking a boat ride from Richmond back to Westminster Pier. For a distinctly rural flavor, take the river boat from Westminster Pier to Hampton Court and spend some time touring this palace. Many of the towns and villages that are popular with Americans in Surrey are within 20 miles (32 kilometers) of here. By taking the train back to Surbiton and changing lines you could pay a visit to Esher, Cobham (via Cobham and Stoke d’Abernon station), or even Virginia Water. Unfortunately they are all on different train lines, but you could visit at least one of them.
If you think you and your family would prefer to live outside of London, rent a car and spend at least a day out of town and skip some of the areas in London. This would be a good time to check out Surrey (around Cobham and Thorpe) or parts of Buckinghamshire or Hertfordshire. If you have kids under the age of seven, then you may want to visit the Bekonscot Model Village and Railway, which is in Buckinghamshire and around five miles (eight kilometers) away from Gerrards Cross. If your kids are too old for this, there are several stately homes (such as Hughenden Manor or Cliveden House) in this part of Buckinghamshire, or you can visit Runnymeade and see where the Magna Carta was signed. For more information see the National Trust website. North of London in Hertfordshire the grand stately Hatfield House was built in 1611, and part of an early palace (home to Elizabeth I in her childhood) can still be seen. Hatfield House is less than 10 miles (16 kilometers) away from both Harpenden and St. Albans, so explore these areas while you are up this way with the car. St. Albans was an old Roman town (called Verulamium), and the Verulamium Museum has some wonderful Roman artifacts.