Beijing is very photogenic, and you could spend weeks wandering around here and still have plenty of things to see. We had 4 days; below are some of my impressions.
The hutongs are old Beijing, neighborhoods made up of narrow alleyways and single-story homes, with what seemed to be community bathrooms. The predominant color was grey, but despite the drabness it was fascinating to walk through and get a glimpse of traditional life. Though they felt calm in comparison to the rest of the city, the alleyways were fairly bustling with electric mopeds, who were constantly honking at us to get out of the way -- because we didn't hear them otherwise.
The Forbidden City and Jingshan Park
The Forbidden City is impressive, and enormous. We spent about half a day wandering around inside. Jingshan Park, on a hill overlooking the Forbidden City, was the perfect end to the day - fun, lively, and with great views onto the Forbidden City and the rest of the city as well. I wanted to skip Jingshan Park and go back to the hotel and take a nap instead (blame jet lag) but I'm SO glad I didn't.
Park Scenes, Street Scenes
Beijing parks are hopping. Mostly with senior citizens -- a tour guide later confirmed that it was the retiree crowd that hung out at the parks. From my vantage point, at least, it looks like they have it pretty good. It was very social, and there were lots of groups singing, dancing, playing games, knitting...you name it. Amusingly, there also seemed to be a bit of competition going on between the various music groups. At one pavilion, there would be a choir singing, and approximately 10 feet away there would be somebody playing music on a boombox and dancing, and around the corner there would be someone playing an instrument. It was quite dissonant, really, but I appreciated the enthusiasm of all involved. In the evenings we would also see groups of people gathered on the sidewalks, seemingly for their evening aerobics, set to pop music. Presumably this was for those with a day job.
As for the streets themselves, we were into all the various ways people had tricked out their electric scooters. (We didn't see any non-electric motorbikes in Beijing, I assume it's a rule to improve the air quality.) Apparently key to making it through the Beijing winter was having mittens and a blanket built into your ride - quite clever really.
A glimpse of ultra-modern Beijing.
I was the only one of our group that made it over to Sanlitun, and that was not because I knew anything about the neighborhood, but because I was trying to go to a yoga class. I never made it due to an Apple Maps fail, but briefly got to see a completely different side of Beijing - a shiny, highly-polished version where you could believe you were in any city in the world.