'Merkin in the UK for 6 years now, and every time friends / family come over, I have someplace new to show them so really don’t let your wife expect to spend 3 weeks and see it ‘all’ or even most of it.
I live in London, so if she’s going to come this far South hopefully some of these recommendations will help. The other recommendations made, especially the Yorkshire Dales and the Peak and Lake Districts (two separate places BTW - the Peaks is full of Lakes and the Lakes is full of Peaks oddly enough) are both close-by Leeds, but for London:
Camden Market. Should be rebuilt by then after a huge fire last week, and I’m sure could use the business. Neat clothes and stuff for shopping, but it’s the people that really make Camden Market interesting - it’s full of goths and punkers and ‘freaks’ who are lovely and weird and fun! Portobello Road open market - kind cool and kitchy, and nothing at all like the movie Notting Hill. Borough Market - wonderful open-air food shopping. Also some excellent restaurants, and you can go from Borough Market along the south bank of the Thames to the Tate Modern, then on to Shakespeare’s Globe Theatre and onwards to Southwark, and then onwards to Battersea Park which is lovely if the weather’s good.
St Paul’s Cathedral and crossing the Millenium Bridge to Southbank of the Thames. Also both the Tate Modern and Tate Britain museum - Tate Modern is just what it says on the tin, but the Tate Britain is the more ‘standard’ art museum. You can also take a riverboat between the Modern and the Britain which is kinda cool. I would also highly recommend the British Museum, the Natural History Museum, and the Victoria and Albert Museum. But pretty much plan on 1/2 a day for each museum (seriously!) and plan breaks inbetween them or you’ll wind up with sensory overload and not be a happy bunny at the end of them.
Regent’s Park and the Regent’s Canal area near it - lovely, also home of a wonderful zoo, and you can walk along the canal all through London and never have to be on a ‘street’ - it’s like a totally different view of London. Hyde Park is also quite cool, although if you go when the sun’s out and it’s warm you’ll be struggling to find a place to sit where there aren’t couples actually on top of each other, but if you go to Richmond Park or Bushy Park, you get a more ‘wild’ feeling to it and both are full of deer and tourists. Bushy Park is also close to Hampton Court Palace, one of the riverside palaces Henry VIII built for his mistress so he could take a river barge down from the Tower, Westminster, or Buckingham Palace or Windsor and see his lady-friend before I think she was executed for something.
You can also see Harrod’s department store in Knightsbridge to see just how vulgar one can become with excessive money and no taste. 
But a big recommendation is for your wife to take an open-top double-decker bus tour. I would say do this in Oxford as well as London; they’re both great cities. And having a guide, plus the hop-on hop-off capability to further explore is quite cool. They’re pretty cheap, and weather permitting quite pleasant, and will give you a guided tour of the most important cultural / historic sites in the given city.
Some other cool cities - I quite like Southampton, but that’s because i’m a fair-weather sailor and love being close to the ocean - without that it’s a bit of a rough-and-tumble city. I also quite like the Isle of Wight, but it’s best done with either a bicycle or a car and tough to do otherwise. I also quite like Wales, especially Snowdon National Park and the Brecon Beacons, but again they’re a bit harder to do without a car. Bath is Lovely, Bristol is historic, York is excellent.
It’s all good, bascially, even Madchester 