Diego Velazquez at the Wallace Collection (Wikipedia)
For first-timers in London, I would certainly recommend that you go look at the famous sites: Big Ben, the London Eye, Buckingham Place, National Gallery, V&A. However, if this isn't your first visit, or you're a resident of this infinitely interesting city, try some of these for a change:
1)The Wallace Collection
A townhouse (quite a large one!), not far from Oxford Street, holds a great collection of 18th century French paintings, sculpture, armour, furniture and porcelain. There are also Old Master paints by Velázquez, Van Dyke and Titian.
Put together as a private collection by the 4th Marquess of Hertford and left to his son, Sir Richard Wallace, a condition of the bequest was that no article can be removed for the building, even for loan. As well as the permanent collection, the Wallace runs special exhibitions and holds occasional talks and events.
For riverside pubs and characterful streets, this is a part of the city seldom seen by tourists. Full of history, in the form of stairs down to the Thames used by amateur archaeologists these days to comb the foreshore; or a gibbet set up behind the Prospect of Whitby pub to commemorate the past presence of the Execution Dock where pirates were hanged; or the statues of the "bluecoat" schoolchildren at St John's Old School - there is much to be seen and a lovely old atmosphere in the this neck of the London woods.
3) WWT London Wetland Centre at Barnes
I love this nature reserve I've visited a few times now, and it's never been too busy. Easily accessible on the 283 bus from Hammersmith station, this centre opened in 2000 and now covers 100 acres of land previously submerged by reservoirs.
The Centre is home to a large number of birds not normally seen in London, and is split into different landscapes in order to provide environments for the greatest variety of species: for example there's a world wetlands, and a pond zone.
Ally Pally is an unlucky but wondrous big lump of a building, and on a sunny Sunday morning, there's nothing better than gazing down from its terrace onto the wonders of the Capital. Having caught fire twice (destroyed completely in 1875, rebuilt and a large part of it wiped out in 1980) enough of the building has now been restored so that it is the venue it was built to be.
For the best exercise, walk up to the front of Ally Pally from Hornsey Railway station. If you'd rather find alternative routes by bus or train or a less strenuous, there's plenty of information on the Palace's website.
5) Dr Johnson's House and Cat
Samuel Johnson was the creator of the first ever English dictionary, and it was in this 18th century house that he compiled it. This is a small, sweet museum just north of Fleet Street, and it's advisable to have a map with you to find it.
After Johnson's sojourn in the townhouse, it became a small hotel, printer's workshop and a social club for the Auxiliary Fire Service during World War II but somehow still has its original floorboards.
Outside the house is a lovely 1997 bronze statue of Johnson's cat, Hodge. His feline friend is seated on a copy of his dictionary, with some oyster shells before him (it was said by his friend Boswell that Johnson was wont to feed the cat with these shellfish).
You do need a very special ticket to get into the reading rooms at the British Library, but you'll find that there is lots to do in the public areas as well.
The largest public building erected in the twentieth century (1998) this new building amalgamated a number of libraries scattered around London. Surprisingly, the British Library as an association has only been in existence since 1973.
There is normally a large exhibition being held - science fiction was a recent one, and in the first quarter of 2012 there's a major one on Royal manuscripts. There are usually smaller exhibitions on the go as well (at the moment that's A Hankering after Ghosts: Charles Dickens and the Supernatural), and I've even watched music recitals there.
This square is just off Oxford Street and so far it's relatively unknown - the thousands per square inch tramping Oxford Street near Selfridge's don't all appear to find this little area, thank goodness.
There are some shops if you really want more of them, including Whistles and Reiss, but what is really the point of this area are the restaurants. Lots of seats outside, many heated in winter, and there is a range of cuisines, including Italian, pan-Asian and Lebanese.
You'll see a sign off Oxford Street pointing towards St Christopher's Place through a narrow corridor - just don't tell anyone else it's there.
Entrances are at Finsbury Park, Muswell Hill and various other points along the route. This Parkland Walk map details them all.
9) St Bartholomew's Church
In my opinion, this is by far the most beautiful church in London. A church has stood on this site since the 1100s and the sense of age is palpable. The smell of the incense remains with you, I think, forever, after having visited.
The church is right beside Smithfield Market, which is a also a beautiful building to visit, and the Museum of London is just round the corner as well.
This museum, situated in a row of former almshouses, specialises in period home furnishings. They have a series of rooms, each representing the furniture, fabrics, paintings and decorative arts from differing periods of time.
There is also a restored almshouse which can be viewed at certain times only, as well as period gardens.