Tokyo is very busy, and it is not easy and safe to run, particularly for international tourists. There are, however, some good area for jogging. If you are a big runner, wanting to jog a long distance in a safe space during your stay in Tokyo, it might be a good idea to find a hotel near by the following jogging routes.
Close to Tokyo train station, this is one of the most popular tourist spots in Tokyo, and a very popular jogging spot at the same time, particularly in early and after work hours. With many jogging clubs running together, this 5km circle course is so popular and busy that it sometimes looks a marathon race ! If you want to avoid the crowd, very early morning or middle of the day would be the best time. There are many hotels around Tokyo station but they are often expensive. If you want to stay close to this tourist spot/running track with reasonable budget, the left side of Imperial Palace might be good. Green icons on the map below, there are Hotel Grand Arc Hanzomon (3-star) and Hotel Monterey Hanzomon (4-star).
If you prefer to enjoy more relaxing jogging in green area, Yoyogi Park is a great place. Close to Harajyuku/Shibuya stations, there are many small paths to jog around in this park (a full circle is about 3km). There are not many hotels nearby this park but Hotel Wing International Premium Shibuya (Green icon on the map) is conveniently located between Shibuya station and this park (6 min walk). Located at the edge of popular and busy Shibuya district, this 3-star hotel is new and quiet.
This is the sports complex area (including Japan National Stadium and Tokyo Metropolitan Gymnasium), and popular for joggers as the path is relatively wide and easy. In autumn season, the leaf of tree changes and the whole street becomes very beautiful. There is Mitsui Garden Hotel Jingugaien Tokyo Premier (Green Icon on the map) in this area. This 4-star hotel is conveniently located closed to 3 train stations (5 min walk) and has decent fitness room and small swimming pool.