You can get really close to old Beijing at the Temple of Heaven, but you have to get there early! Me and my friends were tipped that large numbers of old Chinese retirees (about 400 and above) congregate in the Temple of Heaven park's Southern Gate, opposite Hongqiao shopping complex. Go there at about 5.30 am, you can mix in with the crowds without paying, and watch them practicing swordplay, Beijing opera, tango in the old faded Ming-style corridors. It is a very magical sight.
Better still, at about 7.30am in the morning (depending on season), wait for the ticket booth to open, buy the first ticket and rush in! You will have the entire Temple of Heaven complex to yourself, and we got a taste of what it was like for the Emperor, the sacred silence, the sanctity of the site, all to yourself before the crowds start coming in minutes later. It's worth it, but my best memories are still that sprightly middle aged man and his young dance parter prancing the foxtrot along the ancient corridors, surrounded by streaming rays of morning light. Magic!