Oh, there are so many great ones in London!!! I'm envious that you get to see them for the first time!!! The history here is just insane and the museums are beyond incredible. Have a blast and try to check out as many of these as you can!!!

• Tower Of London –don’t let the high admission fee discourage you from coming here. It’s an absolutely incredible experience that will give you a sense of history like almost no other place in London. If you can, send away for tickets to see the Ceremony of the Keys. It’s a nighttime ceremony that’s been going on for 700 years and it’s not easy to get to see (the tickets go months in advance). Here’s the link to apply for tickets: http://www.hrp.org.uk/TowerOfLondon/WhatsOn/theceremonyofthekeys
• Household Cavalry Museum–its sounds like a colossally dry museum but it’s actually pretty fascinating. The Household Cavalry are the guys you see on horses who guard the queen. 
• Victoria & Albert Museum–if you leave London without seeing the V & A you need to turn around, get right back on the plane, and go see it. One of the most extraordinary museums I’ve ever been to (with a couple of the best book/gift stores on the planet). There’s literally always something great going on here (there’s actually a David Bowie exhibit right now). Try to go on a Friday night when the museum is open late—there’s always a very festive atmosphere and it’s a lot of fun. 
• National Portrait Gallery–if you’re a royal watcher (or even if you aren’t) this museum is a blast and you’ll probably recognize a lot of the portraits (like that horrible one of Kate!). 
• The National Gallery—this is right around the corner from the portrait gallery so you might as well see it. Not as great as say, the British Museum, but still wonderful. Try to make sure you see the famous Stubbs painting of the horse in room 34. 
• The British Museum—if anything ever happens to me I want my ashes spread here. I’ve spent literally days (and days) here and never feel as if I’ve seen everything. The room on the first floor dedicated to the Enlightenment just blows me away and the Rosetta Stone is pretty spectacular, too. This is such an amazing experience. 
• Natural History Museum–I had no intention of ever coming here but I was pretty knocked out by it. The architecture alone is reason to come—just a breathtaking building. They always have a great twist to their exhibits (the last time I went the main exhibit was about sex). Don’t miss it!
• Central Criminal Court (Old Bailey)–this is actually something that I’ve always wanted to see but haven’t yet. Basically you go and watch trials taking place. Sounds completely fascinating to me. 
• House Of Parliament–same as Old Bailey. You get to watch members of Parliament debate (and basically yell at) each other. Take note: only U.K. residents can send away for tickets. The rest of us have to line up and hope we get in after all the ticket holders are seated. 
• Kensington Palace—I was lucky enough to see this place one year before the restoration and one year after and the difference is just amazing. As you probably know, this is where Princess Diana lived and raised her boys and it’s also where Queen Victoria grew up. The last time I was here they had four different exhibits going at once. Truly an amazing place. 
• The Proms Royal Albert Hall—this is a series of concerts that take place all summer and culminate in a “Last Night of the Proms”. It’s a lot of fun and actually a little rowdy and very, very patriotic. Not that easy to get tickets to, so if you can’t get any, try to scout out one of the parks where they show the concerts on a big screen. Really a fun, uniquely English experience and actually pretty moving.