London has some awesome museums, most of which are all free. I highly recommend the British Museum and the Science Museum, and the Museum of Natural History is also definitely worth a visit.
Being geeky, you'll probably enjoy a visit to the Trocadero centre.
If you have money, the London Eye and a cruise along the Thames are really lovely and give you some wonderful views of the city.
Then of course there's all the famous locations which are all free to just go look at, it's not that hard to get to most of them.
If you have lots and lots of money, you should go see a show in the West End.
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For Paris, I imagine you know what most tourist things are there (Eiffel Tower, the Louvre etc) so instead I'll just give you hints for visiting
If you want to avoid the queues at the Eiffel tower, try and go pretty late at night. They'll still be long, but much better than they are during the day and the view at night is fantastic.
There's more than one entrance to the Louvre, instead of waiting at the Pyramid like everybody does, you can enter through a shopping centre to the west, afraid I can't really remember exact directions but I don't remember it being particularly difficult to find. Also if you're under 26 and from Europe, you get free entry - there's a special queue and you just need to show your passport.
If you want to try snails, there's a really good little cafe just opposite the Moulin Rouge and it's relatively cheap, then from there if you follow signs you can walk up to Montmartre and the Sacre-Cour which gives you amazing views of the city and the Montmartre area is really, really pretty (there's also an amazing ice-cream shop there - full of choice)
The Champs-Elysees is lovely and if you start at the Arc de Triomphe you can walk all the way down the Place de la Concorde.
Also you're in luck to be visiting while the Paris Plage is on, there's usually a bunch of activities for that so I recommend googling it and see what interests you.
If you have time, then a day-trip to Parc Asterix is definitely worthwhile, it has some amazing rides and is pretty good value.