London on a budget with teenagers

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So, beginning of August we have 4 days in London.
We're staying in Greenwich but going into London itself on 2 of the days.
I think a couple of museums, looking at the Sky garden, will get a 24 hour river taxi ticket - what else would people recommend for a family on a tightish budget please.
Also are there any places to get cheap theatre tickets on the day?

We've previously done the usual palace/tower/zoo/shrek things, maybe looking for something that the teens will enjoy.
Thanks

Check out fringe theatre like The White Bear.

Fringe

Much cooler and much cheaper.

If they like Hamilton they release a small number of standing tickets for £10 or so each every day around 10am you don't get a seat but it's not too bad as there is a ledge you can lean on and the view is good for what you pay. Obviously not as good as £100+ seats but a great cheap way to see the show.

Thanks for all of the suggestions. I've booked a show, got cheap tickets with the children's theatre week offer, booked 2 museums and the cable car, have loads of walking around cool places to do too. Thanks for all the help.

Pop into Forbidden Planet near Covent Garden to check out all the comics.

Denmark Street for the music shops. It's a short walk from Tottenham Court Road Tube (Also the address of Cormoran Strike's detective agency).

Further down towards Leicester Square is Forbidden Planet which is a comic book/franchise/popular culture stuff. Nerd city! It's on Shaftesbury Avenue. In thd basement is an excellent comic/bookshop.

@crumpet Cross-post!