Advice for 4 day stay in london

If you're flying into Heathrow, just take the Heathrow Express train that is a one way to Paddington Station. Your hotel claims to be within walking distance of the train station. Or, take one of the many cabs sitting out front for the short ride.
If you're coming into Gatwick Airport, you'd take the Gatwick Express to Victoria Station. For the four of you, I'd suggest a cab across Hyde Park to your hotel.
You might check into the London Pass to see if it's worth it to you. The great British Museum and Vickie and Al Museum are free. You might just want to get passes for public transit.
https://www.londonpass.com/london-pass-prices.php

I do wonder why the Heathrow (and Gatwick) Express trains are recommended on this forum, they have got to be mile for mile one of the most expensive train journeys in the world (yes I know it's cheaper if bought well in advance) and unless you are staying in Paddington you still have to get the tube or a taxi to get to your final destination, it's probably the word "express" that sells the very expensive tickets. The normal trains are only slightly slower and are more frequent than the express trains.

During your visit you probably will have a number of questions about getting around London on public transit. Source of all knowledge is the government website which contains an interactive travel planner:
https://tfl.gov.uk/

A comparable source is Google Maps travel directions from point to point. The website link will depend on where you are based.

Thank you for all good feedback
So I hear TFL has more reasonable pricing. Is that true?

What train shall we take to go to Paddington Station from LHR?

And my second question was that is it worth to buy London’s explorer pass for a 4 night stay in London for family of 4?

I have not heard of the “London Explorer Pass.” Do you have a website link? The London Pass can be a good deal if what you want to see is covered by it, but you have to analyze the costs of the places you want to see and determine if the pass will offer a savings.

The Harry Potter Walk is probably one of the offerings by London Walks which is not covered by the pass, by the way.

Do not miss the Tower of London, usually a favorite with everyone and iconic. Go at opening for the least crowds,

I often recommend the Heathrow Express because it is fastest and most convenient if one is staying near Paddington, as this family is. It is not so expensive if one plans ahead and buys tickets well in advance, or avails oneself of an appropriate discount. Children under 16 go free with their parents. And it is a nice, easy, and comfortable way to travel after a long overseas flight, with no transfers on the way. That is important when traveling with children and luggage.

They are too late to take advantage of the advance purchase discounts. However, if their departure from London on 11/13 is also from Heathrow, they can benefit from the DUOSAVER ticket. This is a return (roundtrip) ticket for two adults traveling together. You specify the direction and first date of travel (Heathrow to Paddington) and then the return date can be any day within a month (30 days).

https://www.heathrowexpress.com/duo-saver

The cost is £55 total, bringing the cost of each trip down to £13.75 per adult, instead of the full,fare of £22. And children still travel free. Just be sure and enter the code DUOSAVER. Click on the "promotion code" link to open the box where you type it in.

hey arezou
couple sites to look at: withlocals.com it's kid friendly and some have kids free with an adult.
b-bakery.com is a afternoon tea bus tour thru london and see some of the sights
londonwalks.com
we walked around piccadilly circus, regent street, trafalgar square, buckingham palace, tower of london. had a great time. since the kids are young be careful how far you're walking, take a rest and enjoy an appetizer and drink, people watch.
aloha

The choice between TFL service to Paddington and the Heathrow Express may be influenced by their arrival terminal at the airport. Heathrow Express serves T5 and T3 (which is connected with T2), but not T4. The TFL service serves T4, T3 and 2, but not T5.

King's Cross in London has a new Harry Potter gift shop, near the Platform 9 3/4 I'm told.
St Pancras next door has the clock that the flying car went past in the 2nd HP movie. The British Library (the next one over from St Pancras hotel) is free and has LOADS of historially awesome stuff all in one big room, easy with kids, also a cafe'/lunch counter right next to the room, and a gift shop on the way in.

The kids that age who would stay at the Girl Scouts/Girl Guides hostel where I worked for a couple of months would often like were the Abbey Road time, and looking for themselves on the web cam's recording on their web site, the Leicester Square M&M's store was popular :) and so was the Harrod's milkshakes counter. Depends on the individuals/girls or boys/ interests, etc.

There are SO many free things to do, it's really up to you all, to decide if there's certain things you would be paying admission for that you would need the London Pass for. Many things close on Sunday, so that might be a factor in your calculations to decide if you're getting your money's worth :)

My daughter also loved seeing the HP movie in the IMAX right near Waterloo Station. Good back-up plan for bad weather.

https://www.odeon.co.uk/cinemas/bfi_imax/211/

The trick was to find the path that led to an underground pathway to get under the circular road and to get into the IMAX. We had to go ask a student how the heck to get IN to it :)

Hope you all have a great time, make it FUN :)
-Alison

Thank you all for your feedbacks. I bought tickets for Heathrow express.

Which site do you recommend for buying a HP walking tour. I found this but the reviews are mostly not so good:
https://www.viator.com/tours/London/London-Harry-Potter-Walking-Tour/d737-5227POTTER

and I found this as well:
http://www.walks.com/our-walks/harry-potter-on-location-in-london-town

which walks on the above tour do you recommend?

Thanks,
Arezou

Go with London Walks. No need to buy tickets. Just show up at the designated time and place and pay the guide. (Cash only.)