It depends on the type of the flight. But generally speaking avoid anything departing in the night. Longhauls departing at night may not be so bad, but it's not a good idea really (if you can avoid it)..
Just use common sense. Would you like to take a 2 hour flight that departs at 03am.. No.
If you cannot fly 'redeye' routes (coast to coast in US; depart in the evening and arrive in the morning; timezones help a great deal!) then another option is to park the plane at either home base or at outstation during the night. For example you can depart home base in the evening to arrive to another airport around midnight - then increase the turnaround to park the plane there overnight, to depart again at 0530 (or something like that) back home..