Marcs advice is sound, tho I'm very partial to Rome.
Europe's got zillions of places of interest. One I haven't 'done' is the Al Hambra palace in Spain - it looks awsome!
I can heartily recommend some river-boating or canal adventures.
You get to see the most amazing little towns and cities especially in France which is still -IMHO- the food capital of the world, Lyon in particular.
Tho' crowded, Venice, Florence and Siena are beautiful.
Ditto Paris, Buda-Pest (pronounced 'pescht' I'm told) and Bruge.
The Amalfi coast - 'Italian Riveira' - is where I'm gonna live out my dotage it's so beautiful, but it's VERY expensive so getting a sugar-mama is a good idea.
Lunnun of course, but also Bath and environs, the entire county of Kent, Gloustershire (p. "Gloster") - where I used to live - in a village called Tetbury which is very scenic tho' only about 3 miles (the UK has a thing called a mile which is about 1.6 kms) from HRH Charles who's a bit of a damp squib.
Also the villages of Guiting Power, Broadway, Burton-on-the-water, Stow-on-the-wold, Malmsbury in Wiltshire, Hey-on-Wye in Shropshire I think or Woodstock in Oxfordshire (abbreviated to 'Oxon' but not pronounced that way), Oxford of Course, Cambridge naturally and that great, big domed eco-thing thay have in Cornwall, although people down there are still surprised by horseless carriages and wireless telephony.
I'm told the Balkan side of the Adriatic is stunning, but they always seem to fighting so I've avoided it.
Avoid also Rotterdam, Naples, Birmingham, Manchester, Zeebrugge, Vienna (Vienna I hear you cry) as really there's only about two sqare miles of enchanting old stuff and the rest is just a post-war industrial wasteland.
That's all I got for the moment but if you are prepared to fund a tour guide, I'm happy to tag along!