Most - but not all - of the state-owned museums and Art Galleries are free to enter, but they also usually have paid for exhibitions running as well. To name a few:
The Natural History Museum: a must-visit for the dinosaur exhibit - get there early in the day to avoid the queues - and the incredible collection of moth-eaten Victorian stuffed animals.
The Science Museum: just around the corner from The Natural History Museum, great for interactive stuff
Victoria and Albert: wonderful if you like design-led exhibits, such as interiors, fashion and jewellery through the ages. Make sure to look up as you go in, there's an amazing blown-glass chandelier... They often have activity packs for kids, check the website to find out about this.
The British Museum ; fantastic for all things Ancient Egypt and I think also the Elgin Marbles - statues originally nicked from the Parthenon in Athens. (Am sure you will you know this but I prefer to go with too much information than too little... You might have noticed that about me by now)
The London Transport Museum; went there with the Boys and it's brilliant, much more so than it sounds. Would quite like to have been there without them and spent more time if I'm honest...
also,
The National Portrait Gallery, Trafalgar Square. Great location and it does what it says on the tin...
Tate Britain; again, good location (by the Thames overlooking Battersea Power Station, very iconic), and be sure to check out the paintings by Burne Jones (if you like that sort of thing, which I do), and any Turner on view
Tate Modern; probably don't need to explain this one, and again, a great location on the South Bank. Be prepared to encounter lots of kids at this one (and not understand too much of what's on show), but children seem to love it.
Shopping / Taking in the atmosphere
AVOID Oxford Street at all costs -
unless you have a specific shop to go to or want to visit
Selfridges, which I admit is worth the trip, or
St Christopher's Place (near Selfridges) which is quite nice for a pavement cafe experience. Of course, Hamley's on Regent St is popular with the children, try not to go at the weekend though as it gets crazy. Whilst we're at it, in Knightsbridge the locals prefer
Harvey Nichols to
Harrods, but as they're almost next door to each other you might as well do both at the same time, and Harrods food hall is always worth a look.
Instead, trek down the
Kings Road, starting at Sloane Square Tube station, stopping at Duke of York's square for an overpriced coffee and cake in the sunshine at Patisserie Valerie or the Italian deli/restaurant next door. Kings Road does have all the usual chains but also a lot more one-off boutiques so doesn't feel quite as chain-store as a lot of high streets in the UK.
For a high-end shopping experience visit
Westbourne Grove in Holland Park; just a small parade of shops but very nice and with a couple of nice cafe's to visit. This can be combined with a trip to
Portobello Market (go early), but be sure to leave your wallet at home because the prices are generally outrageous...
Covent Garden; Again, leave the wallet at home (nothing too unusual to buy there and mostly over-priced), but just walk around soaking up the atmosphere of this converted old fruit, veg and flower market; if you're lucky some of the performers from the Royal Opera House will be busking in one of the galleries in their lunch breaks, which is always a treat. This can be combined with a trip to the London Transport Museum, which is in the South East corner of it.
I'm also told Hampstead is nice, but have never spent much time there (North London, darling? Are you sure?).
Open Spaces
Hyde Park - obviously. Take a picnic and walk along the Serpentine (or stop in at The Dell or the Lido Cafe for a not-too expensive lunch in lovely surroundings). The cuisine is not amazing but much better than it used to be and the views make up for it. The
Albert Memorial was recently done up and is also quite impressive. If you have young kids be sure to visit the Peter Pan statue and the
Princess Diana playground in Kensington Gardens (essentially part of Hyde Park, at the western end), and on a Sunday morning they often have model boats on the Round Pond - also good for kids. The actual memorial fountain to Diana is a bit disappointing, but can be seen from the Lido, and if it's warm enough lots of people paddle in it.
Holland Park - a hidden gem at the far (western) end of Kensington High Street. Visit the Japanese Garden, watch the peacocks, let the kids run off excess energy, and pick up a sticky flapjack from the cafe under the Arches. If you're feeling flush book lunch at The Belvedere restaurant.
Battersea Park - south of the river so a bit more of a trek but still lovely, green and open and has a great - very small-scale & low-key - zoo. You can easily while away a morning here.
St James' Park - if you visit Buckingham Palace then you're practically there. Am coming across as a cafe freak but the restaurant in the middle of it is quite nice;
Inn the Park. Very romantic if you're there in the evening, though they are not always open then. Otherwise it's open during the day for sit-down meals or you can sometimes pick up a picnic lunch there.
Walk along
South Bank from Westminster Bridge past the
London Eye, (worth a visit, pre-book online to avoid some of the queues),the London Aquarium (OK, doesn't compare to what they have in Florida etc, but not bad for a central city one), past the National Film Theater where you will see lots of street artists practising standing dead still, along to
Gabriel's Wharf for yet more cafe culture.
Food
Pretty much anything goes, but here are a few ideas on chains:
Carluccio's - good Italian food (the chocolate ice-cream is fantastic), and great with kids as they do a very reasonably priced menu for them and provide crayons etc to keep them happy. There's one opposite South Kensington tube station if you want somewhere to go when you visit the Natural History Museum / Science Museum / V&Albert Museum.
Wagamamma's (a chain you'll find almost everywhere) for decently-priced yummy Japanese Noodles and dumplings (no sushi). Refectory-style bench seating and the kids usually love it.
Paul's patisserie for delicious French treats (their macarrons are to die for and of course not diet). Try also their hot chocolate which is so thick you can practically stand a spoon up in it.
And obviously you must have a curry, but these are not usually chains so you'll need to find your own way on that one, and whilst we're talking about One-off Eating Experiences:
Head up to
Soho and
Bar Italia on Frith Street in the late evening if you want a coffee soaking up the bustle of London out on the town, and if you're feeling adventurous and in need of a bagel at 3am take a cab to
Brick Lane and the
Beigel Bake where you can get incredible hot salt beef-filled beigels or yummy cakes 24 hours a day and for an amazingly low price.
For more expensive meals try:
The Wolsey on Piccadilly - French bistro style and they always keep a few tables in a section at the front free, and you get to celeb spot too
Hakkasan near Tottenham Court Road - Delicious Chinese food, lots of media wannabe's
The Enterprise (more of a pub / bistro) on Walton Street in South Kensington. Not as expensive as the first two but usually pretty nice food.
Pubs
Not that I get to go too often and these are west London based, but they are a good start and also serve OK food:
The Grenadier, 18 Wilton Row - hard to find, near Hyde Park Corner, but worth the effort. They serve fantastic bloody Marys on a Sunday morning and if the sun is shining have a couple of nice tables you can sit at outside with the children...
And that, I think, is quite enough for the moment...
Update:
Or it was, until I decided to put a McLinky related to this
in the post above... So if you want to share your own ideas on what to do in your home town, please feel free to post and put a link in the list.