London - Help needed!

[Castlecould]

Hi all
My lovely son has surprised myself and DD (11) with a trip to London and I was hoping some of you could help with the travel logistics for us first timers.
We arrive at Gatwick at 8.30am and our Hotel is the Premier Inn Old Street N1. We then fly home late the following night from Stanstead so if anyone could give any advice on the best way of getting to and from the airports to the hotel that would be great. Is there a travel card type thing that can be used against all public transport or am I best just using my contactless card to get around?
As we'll have 2 almost full days I was thinking we could head into central London the first day to do some sightseeing and generally just walking around. Is there any attractions that are really worth paying for - The Tower Of London and London Eye are possibles but open to new ideas and suggestions?
The second day I thought we could do the Science and History Museums. Does this sound a good plan and if anyone can help on travel from our hotel to Central London and to the Museums that would be a brilliant help too.
Thanks!

"Generally just walking around" is the best way to see London. Get a good street map, an A-Z type, not a tourist map.

Or the top of a bus. Get the normal red buses, not a tourist bus. Use the tfl.gov.uk website to look up routes and plan a jouney. The no11 and no15 routes are good for sightseeing. DD might enjoy doing that.

The tfl site will also tell you about payment options.

Not sure I'd do the Tower on a first visit when you only have limited time. What I would do is go down to the Embankment there and look at it from the outside, and see Tower Bridge and the river. Then get a bus or walk through the City and look at St Paul's. Then bus down to Trafalgar Square and walk through St James's Park to Buckingham Palace.

If you have time at Traf Square you could pop into the National Gallery or National Portrait Gallery. The new Foyle"s bookshop is 10 min walk up Charing X Road from there.

Try to fit in a Tube journey, for the experience.

There's a huge amount to see and do though, so whatever you do, you'll only scratch the surface.

hi! you can consider getting a London Pass. this gives you discounts to lots of the attractions in london, and it also gives you the freedom to travel where you like, as you use it as a ticket. however, to get to central london from gatwick, you will need to take a train to london victoria station. on the way home, you can get a coach or a train to stansted. all the best x

I meant dd might enjoy planning journeys using the tfl site, not specifically getting those buses - realized I wasn't clear!

I believe you can pick up the Stansted express train from Liverpool Street station, it's a short walk from Old Street (about 15-20mins mainly straightforward). There's lots to do in the area you are staying, if you walk towards shoreditch. You could also walk down to Bank from where you are staying, cross the river and check out the sights along the Thames. Southbank is lovely.