For the London portion of my trip I would like to do this: Day One: Arrive in London at noon, go to Tower of London; wander around London (Big Ben). Day Two: Westminster Abbey, British Museum; Dinner / West End play Day Three Choose what we want to see (perhaps Victoria/Albert Museum, Tate Modern) Go to Paris I don't know if I can cram more stuff in or if this schedule will be fine. I don't want to overschedule because I want to save energy for the rest of my trip, but I want to see as much as I can.
Big Ben is a block from Westminster Abbey (and the Horse Guards) - so you do those on same day (Big Ben is a two minute walk past); Tower of London is in East; British Museum, just North of Leicester Square Trafalgar Square area so doesnt fit in with anything else you listed; Tower of London, City and St Pauls are close proximity, comfortable walking distances. Victoria and Albert Museum (and related Museums) are West of (but convenient to) Kensington, kensington Plaace; Hyde Park and Harrods- a bit much for one day. To get the most out of every day, I would (and do) walk between my planned visits
I would recommend starting a day at the Tower, rather than getting there midday... lineups grow and grow, and it just gets more and more crowded. It's much better to be able to dash in first thing in the morning, see the crown jewels with no one around (guard let us walk backward, lol), and see things at your leisure, without being overly crowded. I would take the National Gallery over the Tate Modern any day, or even Tate Britain over the Modern, but that one is up to your taste. On that first day, if you've ditched your bags, I'd highly recommend a bus or walking tour, especially if you've never been to London. Or, The British Museum is just always busy, might be better to flip it and the Tower.