This is a loaded question – figuring out what times you will run AND what time of year you will run. You need to consider the time of year for weather and for sunrise/sunset times. You also need to consider these for clothing/laundry purposes and for safety purposes.
I love winter running and am not afraid of the cold but I’m not so sure I’ll do it in the middle of our Minnesota winter – too much clothing, laundry and time spent getting dressed, warming up and getting undressed again. I liked doing it in the fall because it wasn’t humid or extremely hot, yet I didn’t have a ton of laundry – I was still able to wear a tank and shorts or capris (at night). So, consider what your seasons are like – if you live down south, winter is probably the best time for you to do it. If you get extreme winters like me (wind chills of 40-50 degrees below zero) winter may not be the best time.
As far as time of day goes for doing your first run, I spent a lot of time figuring this out and writing down different scenarios.
I preferred getting adequate sleep leading up to my first run. I’ve heard of people starting at 8pm or 10pm (or even 6pm) and starting tired/being drained after being up for a full day. Starting at 2am allowed me to go to bed early and sleep until 1:40am. Then I could go back to bed between my 2am and 6am runs. I considered sunrise and sunset times when planning out my run times so that I would finish a run at sunrise and sunset. Then I only had two runs in the middle of the night. It depends on the time of year, but if you ran at 8pm in the dark you would also have a dark run at 12am and 4am. I thrive on sunlight, especially when we have less of it starting in the fall, so maximizing sleep while also running in the light as much as possible was important for me. I also worked around a vet appointment and meetings/calls.
After all my planning and scenarios, running at 2am, 6am, 10am, 2pm, 6pm and 10pm worked best for me, and I did enjoy these times.