I have read annual livable city ranking by Monocle magazine before.
Top cities were Helsinki, Oslo, Copenhagen, Tokyo, etc. Singapore was around 15th.
Import element for choosing where you live would be different.
For example, number of good restaurant is very important for foodies.
Number of good museum is very important for art fans.
Now, I am getting into running. So, I want to think about it as a view of the runner.
First, I want to mention about the cities I have lived.
My home town. I lived over 20 year, mostly lived in country side, Tama district. I lived in Shinagawa city which is located in Tokyo 23 district.
The most important and charming element is security. Even in the midnight, you can run everywhere alone.
There are plenty places of running, famous 5k imperial palace, along Tama river, Sumida river, yoyogi park, Kinuta park etc. However, there are few track around the central. Most famous one is Oda field. I heard it is always very crowded.
There are many sports gyms too. So, being member seems good instead of running outside because there are four seasons in Tokyo. Winter is very cold, Summer is very hot. In addition, there is rainy season and typhoon season.
So, The period that you can run comfortably seems very short.
Usually People in Tokyo are very busy. Time for running would be restricted. Work life balance would be key point.
You can enjoy trail running in Mt. Takao, Oku Tama area, in Tokyo. It would be quite good point. You can also go to Saitama and Kanagawa for other trails.
There are many races and time trials around Japan. So, I think you can enjoy many types of running. Most important thing is having running time with working hard.