I'm in London all day tomorrow

You can't beat an afternoon naval gazing imo. Have you considered sitting in a pub and getting drunk?

Its seemingly grim daarrrn sarrrf
I caught some region news this morning, well regional to Lon-Don anyway.
They reported that over 400 people a day are being made homeless down there....wonder why?

We just love the great outdoors.

London Transport Museum is worth a visit if you like that sort of thing

http://www.ltmuseum.co.uk

if you like planets you'll like the Royal Observatory at Greenwich.

Is the Naval Museum still going? I thought it went belly up.

You could go on a Jack the Ripper tour ?
Museum of London not worth it imo.
British museum a lot better.
Globe theatre on the South Bank's worth standing outside and taking a picture, even just to pretend you've gone back 400 years in time. Whilst you're there you could visit HMS Belfast, not something you'd do everyday, this time of year around 4pm they take in the last batch. Summer I think an hour or two later
Camden Lock is crawling with filth offering class A drugs so brazingly the police just can't be bothered to keep arresting the same people and let them get on with it, maybe it's a bit different now, but the eclectic shops and markets all in one place is a place like no other in the country.

Was on a river cruise along the Thames one summer and the boat guide, or whatever they're called, said as we passed the Tate modern, "and on the right is the Tate modern which is free entry, and when you go in you soon  realise why it's free entry, and as the name suggests it contains modern day art, also known as crap" he was like that the whole way.

Tate Modern, well worth a visit imo. Museum of London quite good as is the above mentioned transport museum. If you want to see some very good modern art for free go the Richter exhibition at the Marion Goodman Gallery.
Enjoy your day :)

London has some of the best museums and public galleries in the world, and many of them are free.

IMO, of the big ones, the best are:

Tate Modern (well worth a visit)
National Gallery
Natural History Museum

Worst are:

Tate (think it may be Tate Britain these days)
National Portrait Gallery (don't even think about it)

But maybe explore your sister's homeland a little. It has a few biggies - the Royal Maritime Museum/Observatory/Park area is quite impressive, and there are lots of little bits and bobs of mainly naval history...

http://www.secret-london.co.uk/Greenwich.html

Depends whether the minutiae of history interest you, I suppose.

Mr Eboue try and get a copy of Timeout magazine which I believe is free these days, it used to be a great reference as to what was happening during the week. They also have their own website http://www.timeout.com/london

Other than the ones at Lords and the MCG I don't think I have ever been to a museum because I wanted to.

Madame Tussaud's has to be worth a visit.

Get one of Boris's bikes £2 for the day as long as you change every half hour.

Does the Emirates do a stadium tour?

I'd recommend the Stamford Bridge tour, even to non-Chelsea fans.

Time Out is free, but a pain to reliably get hold of these days. It has led directly to some of the best and most rubbish nights of my life though.

We used to play Time Out bingo. Met up in any old pub, decide what to do in Time Out over a pint, and do it.

I used to love it HM but you never saw it north of Birmingham railway station, since it went free I've never managed to get a copy.

Our favourite game was actually Yin Yang, which required a bit of organization to get away with if you were going to get away with it. Just had to do two diametrically opposing activities in one day.

My best was to go to the smart enclosure at Henley Regatta (ties and blazers), hop on the last train back to Paddington and go to a rave between the canal and railway sheds somewhere around Wormwood Scrubs. I'm still known as 'Chinos HM' in a certain pretty small circle.