Have lived there twice so I may not be a good candidate for a rec, but.... since you asked:
1) Underrated: it's a city of amazing parks -- Hyde Park, Regent's Park, St. James' Park, and my personal fave, Hampstead Heath -- set aside several hours and just go explore. Each park has its own special features and they're all wonderful.
2) Wish I had done? Well, I've ticked it off the list in the years since I first visited, but Little Venice is amazing and the Waterloo Vaults are worth the trouble to go check them out.
I have a list like 10X this long depending upon if you are a foodie, music geek, history buff (esp WW2), etc. Have fun!