London itinerary with 5yo DS

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hoping for some help and suggestions for 3 nights in London just me and my DS(5). Staying near Covent Garden.

Tuesday (we’ll be up from 5am so museum might be ambitious)
10am arriving into LHR and tube to Covent Garden to drop bags.
wander around and get lunch somewhere nearby
2pm Transport Museum

wednesday
10am skygarden

2pm History museum

thinking we could wander to Borough Market after Skygarden.

Thursday
no plans as yet - open to suggestions

Friday
No firm plans yet except…
3pm pick up bags from hotel to head to LCY for 6pm flight

Also thinking about booking a show but not sure what to pick and wondering if might get better value last minute - isn’t there somewhere in Leicester Sq?

Wow - thank you everyone.

So I’ve booked the Science Museum and wonderlab for the Wednesday morning. Have NHM booked for afternoon but not going to mention it and play it by ear depending on how we both are feeling - Diana Memorial garden on provisional agenda too.

Borough Market is off the agenda. Sky garden too.

going to look up other suggestions now.

thank you everyone.