Hi Dariusz
If I can make a few suggestions:-
Your probably want to get away from the full Moon (24 Dec and 23 Jan). Ideal might be early in the first quarter - say 10-14 Jan. In that way, your son can see the partially lit moon (and the dark side is lit with earthshine earlier - say 9 and 10th?) before he falls asleep
If he stays awake, then the Moon should have set mid evening and you can see the stars etc.
Good time to look for satellites is that first couple of hours after sunset when the low ones are still catching the sunlight.
Shooting stars (meteors) - I don't think there are any expected showers, which are best seen in the few hours before dawn. But there should be a few sporadic meteors - up to 5 per hour - at any time of the night. You just have to be lucky.
Locations - sorry I don't really know, but what about a visit to the Magellan Observatory:-
http://home.goulburn.net.au/~magellan/
Good luck and have fun and drive safely!
Eric
