What's the best time to go to the gym?   

time that does fits to you.

it depends.... if you have a sexy gym mate then why not go when she go in that time... you might know you can work it out there and it might get you fit too...

Hi ritchel! If I were in your shoes, there is no way that I can have the energy to go to the gym after working night shift. I guess, the best time for me is before I work and then will have an hour or two of rest before I go to work so I can have enough rest before my shift. This is what I think will work for me and hopefully it will work out just fine for you.
Take care and have a nice day!
lovelots..faith210

For me, working out early in the morning works good for me and with the schedule you gave, I think waking up and dragging yourself to the gym as early as 6 or 7am is good enough. The very reason why I work out in the morning is that it keeps me alert all day long, though at start I really didn't like the sore feeling I had all over my body. A 6 hour sleep at night might be good enough already and you can still go back to sleep after you go to the gym maybe for an hour or two.