Regent's Park in London lives up to its name and is quite royal, boasting rows of manicured flowers and plants. (There's also a theater, zoo, and walking paths.)
I always make a beeline for the Rose Garden: a circular garden chock-full of roses of various fragrances, shades, and shapes. Benches border the garden and are picturesquely linked by vines and even more flowers. The BBC tower looming in the distance makes an interesting contrast but reminds you that you're still in the middle of a city. Those with allergies, beware.