I recommend:
- The London Dungeons. It’s awesome if you like kind of scary things, but also very interesting history-wise.
- Warner Bros Studio Tour is a must, if you like Harry Potter.
- Any show on the West End. Whether it’s a musical or a play, it’s always worth seeing something. Also ticket lotteries can get you really cheap tickets (but not guaranteed). I recommend The Play That Goes Wrong (it’s great for everyone, whether they enjoy theatre or not), or The Book of Mormon (it’s a very funny musical).
- If you want to see all the iconic buildings London has to offer (Buckingham Palace, Tower of London, Westminster Abbey, Tower of Westminster (Big Ben), London Eye, Trafalgar Square) go on a sightseeing bus tour. I’m pretty sure you can get on them from anywhere in the city centre.
If you want anymore suggestions, let me know. I’m not far from London, so I know a few good places. :3