Which London Airport to fly to

I'm planning a short trip to London, probably next month and taking daughter to see some of the sights as apart from a quick walk round London when on business she has never really seen London.
I am trying to plan a trip for maybe 2/3 days and definitely want to show daughter the National History/Science Museums which are nice and close to each other plus The Tower of London is on the definite to do list.
From Edinburgh we can get flights to all the London Airports apart from City I think.
Squeezy Jet flies to Luton, Gatwick and Stansted for not a lot of pennies (will need those for getting accommodation!). My question is which do you think is the best option for then getting into the centre of London? I'm thinking about booking accommodation in the Kensington area which is near the museums so handy to get bus/coach/train to that area.
It is almost 40 years since I worked in London so will be in the same bracket as your typical tourist I expect, headless and clueless as to how best to do things without being fleeced rotten!!!!
Any other tips advice much appreciated. I can remember pretty well how to get about on the tubes which I would doubt have changed much. Still dirty smelly and either boiling or freezing plus zero chance of a seat.....now I remember why I was so pleased to stop commuting to work!
Also can anybody tell be when the Christmas lights go on? While I am no fan of Christmas the lights in say Oxford Street and the shop windows of the big department stores were usually pretty amazing many years ago and I expect they still are worth seeing?

 

Personally I'd base my decision on which is cheapest for the times I wanted. It's a while since I've been to London but I believe the local trains and underground system very effectively connect it all together, as long as you don't try to travel at peak time ( like before 9 am or again around 4pm to about 6pm). Or if you do want to travel at peak time, take a heavy ambag and leave your morals at the airport.

 

Heathrow and Gatwick both have easy transport links to the west end. I cant speak about Luton or Stansted as I don,t use them.

 

Thanks all, will do my homework. Now can you recommend somewhere nice with comfy beds ensuite with bath if possible, easy walking distance of National History Museum, has good grub and quiet for under about £150 a night for 2 people? You'll be doing well if you can. Aghast at the prices and some hotels from the look of them I wouldn't suggest to my worst enemy. Is the Paddington area still as grim as it used to be? I'm so out of touch that no doubt some places that I would remember as really nice are not now and visa versa. While I am WAY past my sell by date and would be of no interest to white sex slave traders, daughter is very attractive and blond so really don't want to be in some god forsaken area.

 

@silu were either you or your daughter in the forces ?
If so the UJC and the Victory club are 4/5* hotels £20 per year membership, rooms £30 pp

 

Thanks @Jack McHammocklashing but no go. My best friend's husband was in the Army so maybe if I was going with her but otherwise not a hope. Thanks too @shiney, had a look, great local and do have a room for the potential date. Over £150 but not too much over so for London not that bad.
I looked at a hotel I stayed in years ago which was nice and almost swallowed my computer, it's £505 a night and that isn't for the most expensive rooms. You do get Sky TV and Sky Sports, big b deal. I ain't going to London to watch TV!
I'll do a trawl of Tripadvisor and draw up a short list. Seems bonkers that you can get a flight from Edinburgh to London ...well Luton/Stansted for less than £30, yet you aren't going to get any change out of £150 to lay the head in fairly grotty accommodation. Oh well it's offset a bit by many attractions being FOC and it'll be a fun couple of days hopefully.

 

I can recommend The Tower Hotel (next to Tower Bridge) was £150 a night but this was a couple of years ago, from there you can do The Tower Of London (Right next door) also
can recommend a visit to Tower bridge as well, steeped in history, don't forget to walk across the top of the bridge the views are fantastic

 

Cheek but quite correct. I have a feeling that I shouldn't ask how to get into The Tower for free?does it involve aqualung or waders?!
Had a look at the prices for flying into Heathrow and they are triple or more! so looks like either Stansted or Luton. Had a look at The Tower Hotel @intel. prices aren't too bad for such a central location. I'll PM you with a few queries, thanks very much.

 

Using the method in this thread you can get a train from Edinburgh to London (Kings Cross) for £15 (£30 1st Class), and same cost for return http://www.hotukdeals.com/deals/15-...30-1st-class-virgin-trains-east-coast-2522882 Might be worthwhile comparing times & costs against Flights + travel into London

Example: