Several years ago I did all my long runs at night. There was a heat wave on and I waited for the sun to go down. A lot of runs were from about 10:30 pm to 1 am. One time I did a half marathon starting at 1am, done about 2 am.
I found three places to run at night.
On the high school track. I would walk the track first to make sure there was nothing on it, and there was enough light from the town so you could see the lines. When a full moon was out it was surprisingly bright.
At the airport. It is a small, unstaffed single strip. 3,000 yard straight-aways. It was also had guide lights on the side. I wouldn't use it if someone was tinkering with their plane, but almost nobody used it after dark so I had it to my self.
A frontage road at the industrial park. It was an uneven dirt road but pretty much the whole distance was lighted by street lights. I did have to explain myself to the cop but he gave me no grief.
I would not suggest a woman run at those times unless they are in a group.