During my first visit to Beijing I spend one morning wandering around the Summer Palace, listed in the UNESCO World Heritage List.
Although I would not list it as a peaceful place (it is always pretty crowded, especially if you are lucky enough to hit a sunny day), it is definitely in the must-see-place list of Beijing.
Except from the charm of buildings and water, you will find yourself fascinated by small circles of old people playing board games or cards, enjoying the sun and setting the rhythm of their days according to the opening times of the parks.
To know: entrance is 20 Yuan (2.5 euro more or less), definitely worth a visit especially in sunny days. You can relax or stroll around ancient pavilions, mansions, temples, bridges and a huge lake. It takes 2-3 hours for a nice tour.