In the US there were a lot of places that seemed like this to me: Martha's Vineyard, Cape Cod, Boston, LA, SF (although it also has nice sides to it, especially the bay and geographic position), Seattle, Florida, and a bunch more.
In Europe I was disappointed by: Venice (pretty, but disney-like), Budapest (fairly pretty, but unpleasant people and atmosphere), most of Switzerland (deadly boring, expensive, and stiff unpleasant people), Oslo, Stockholm and Copenhagen (they are not all equally bad, but they're fairly boring and overpriced, and not particularly beautiful), and Manchester and Glasgow (basically dumps), and partly London.
On the other hand, there were some places mentioned by previous posters that I really love. Rome, Florence, and Capri, for example.
I think lots of tourists make 2 basic mistakes that contributes to them finding a place less lovely than it really is:
1. In general, don't go to European touristic cities like Rome from mid-June to mid September! You are going to be overwhelmed by masses of tourists and heat. These places are 10 times more pleasant in May or October.
2. Don't stick to just a few small most famous and obvious areas. Most tourists are sheep and concentrate only in these few streets. For example, I was in Florence in early June 2 years ago. Within a 5-10 minute walk radius of the cathedral and the Piazza della Signoria till Ponte Vecchio it was like a zoo! Full of masses of tourists, you could barely walk. Once you went beyond that radius you found yourself in the company of locals and a very few tourists here and there. Prices dropped in restaurants and shops and you could easily find authentic affordable food and products. You might think I am talking about uninteresting suburbs.But, no, these were still central areas, full of beautiful palaces, interesting shops, and lots of churches with famous frescos, and various attractions. It was just a short walk away from the TOP 5 attractions area. Don't behave like sheep and you won't get slaughtered...