First would have to be San Francisco, a family favorite now for 166 years. SF and the Bay Area is one of the stunningly beautiful areas any place and full of interesting things to see and do. Seattle, Vancouver British Colombia, and Auckland, New Zealand fall in this same category of very beautiful water cities.
Christchurch (at least before the devastating earthquake) was a lovely city down south, as is New Zealand's capital, Wellington. New Zealand itself is a simply stunning country of diverse beauty and fantastic people.
Riobamba in Equador is a lovely provincial capital.
Of the great cities of Europe, Prague is probably the single most beautiful, never having suffered the ravages of war. Since the fall of Communism, it has apparently acquired some Western commercialization which was not there earlier, but it has beauty, great people, lovely treasures, and great beer.
Of the German cities, Berlin and München (Munich) are magnificent, full of about every superlative one can muster. Great artistic and intellectual and musical treasures; great people; great ambiance; ease of travelers' assistance. Also, my personal favorite is Nürnberg (Nuremberg) for its sheer rebuilt charm and wonderful, serendipitous things which would happen every time I visited (I lived nearby once upon a time).
Barcelona is lively and interesting. Any city where the curtain rises at the opera at 11 p.m. is my kind of city!
Copenhagen has great food, great shopping, nice people.
Istanbul is fascinating and an obvious cross-roads (watch the old movie "Topkapi" before visiting it!)
Almost any place in Italy is fun, but Florence is the birthplace of the Renaissance and a must-see city
In the United States, Santa Fe is a crown jewel, as is that whole northwest corner of New Mexico.
Los Angeles (Herb Caen said it definitely about the City of the Angels).
Our own nation's capital Washington, D.C., is a fantastic city. Three cheers for Pierre Charles L'Enfant.
If you are a skier, probably no single destination offers more options than does Salt Lake City, itself a pretty desert city nestled against a mountain range.
San Diego has remade its downtown and is quite a fun place to visit.
And, Fresno, the agricultural capital of the world and gateway to Yosemite National Park, Sequoia, and Kings Canyon Parks, has much to commend it, including summer evenings not to be excelled by any place else in the world.
Boulder, Colorado, home of the University of Colorado, is sort of a Berkeley east; totally charming, beautifully nestled against mountains.