Ok, send me your alternatives and other suggestions, but for a personal favourite place on the planet I have to go with the Marie de Medicis fountain in Paris' Jardin du Luxembourg.
I'm guessing that Thomas Francini - the man who drew up the plans for it in the 1600's - could not have the imagined the happiness that his creation would elicit in a dorky Canadian tourist some 400 years later. But in case his descendants read random blogs about travel, thank you M. Francini. Sincerely.
The place is just steps away from busy St-Michel boulevard in the heart of Paris, but it is an almost silent urban oasis any time of day.
It is lined with chairs for anyone to sit down and eat lunch, read a book, draw, make out, take photos, contemplate life, meditate, or just plain sit and drink it in.
The first six photos here are all from the exact spot of the fountain itself, shot from various angles and one with a Hipstamatic lens; the others, from the Jardin du Luxembourg overall.
I also babbled on about this place almost a year ago in a similar post, so I will let the pictures speak for themselves from this point onwards.