What is the recommended time of day for meditation? Does Buddhism have any recommendation for particular time of day for meditation? 
Can I meditate before going to sleep at night if I don't feel drowsy before I go to bed?

Is there any Sutra which talks about this?
No such recommended time. Especially if you are doing Vipassana meditation, you are advised to practice Samma Sati all the time. But early morning(just before dawn) is said to be a good time for meditation since the world is still sleeping and the mind is very clear and less distracted. So you can easily attain Samadhi. You'll find that it's a very good time to study as well. You can easily memorise things. All the Buddhas have attained enlightenment just before dawn as I've heard. Yes, you can do meditation before going to bed. If it's Vipassana meditation, drowsiness won't be a problem as you can meditate on the drowsiness. Some people with insomnia try meditation at nights to help them fall asleep.