I really love running. Please do not mistake me for an extremely dilligent, somewhat crazy, every-dawn-a-day running machine. I wish I was that motivated. Instead I run when I manage to get myself out of bed or decide to not waste my evening online.
You will not find many people running throughout Tokyo at various times of the day because everyone is either taking care of their children, working, or a tourist (sorry, that's a completely untrue generalization, but is part of the reason I think random runners are not common). I have seen the occasional snazzy-sports-wear-clad runner running around the city in the morning or evening, but compared to my experience living in Hillsboro (OR) and Cambridge (MA), it's not that common.
My host family luckily lives between two rivers, and there are lots of parks/public space around rivers in Japan, so I have been able to go running whenever I choose and am rarely alone. Bicyclists far outnumber runners/joggers/walkers, so there's an unspoken law that slow, non-wheeled people stay to the far left so that speedy cyclists can zoom past.
Sometimes my host mom joins me on a run. Here's a photo of us (more like a photo of the running path + scenery):
Sometimes my host sisters join us with scooters or skate-boards, though not recently as it's really cold out. Here we are when it was not cold:
One thing I do recommend, whether or not it is socially common, is to run in places you vacation to (or just new places). I find getting up early for a run on vacation is much easier than a regular school/work day and when you get yourself out and exploring early, you can scout the scenic places and basically have the town/city/local to yourself.
About three weeks ago (I think) CIEE went on our big fall trip to Hiroshima and Miyajima. I got up Sunday morning to run through the Peace Park of Hiroshima and it was so much more thought-provoking than walking through with tons of people milling about and taking photos (I get distracted people watching). I stopped a few times to look at details on memorials that caught my eye or to offer some silent wishes for peace to the young, innocent victims and their families.
Monday morning I went on a fabulous run through Miyajima. I went running around 6 AM, which is not that early compared to city life, but the entire place was deserted when I started out. It was so quiet. The sun hadn't risen yet and as I approached the 厳島神社 (Itsukushima Shrine, a very famous shrine in water - if you google it you'll be like, "oh yeah! I've seen photos of that before." Probably.) the flood-lights that lit it through the night went out. And I noticed monks walking around the base of 厳島神社 (normally not possible because the tide comes in the whole day and surround it with water) which made me realize how giant that Tori gate really is. I watched the sun rise accross the bay waters which was beautiful, then ran up to the near mountain where red Momoji leaves covered the ground and I felt like I was running through streams of blood (but in an unreal, beautiful, artsy way... not real blood). As I ran back to the hotel, the few locals trodding through their morning duties looked surprised as I ran past, but we still bowed to each other with the greeting, "おはようございます。" (I, a little breathless and awkward while trying to slow down but not stop running).
All in all, it was a great trip and I am very glad I went running each morning there!