Here you can see the moon phase and rise and fall times for this and next month.
It is best to look at the night sky after the moon has set or before it has risen.
In general, the best period to experience the night sky is from 5 days before the new moon to 5 days after, but it depends on the season. So note rising and setting times, if the moon has set and the sun too, it's not a problem. And if the moon does not rise until a few hours after sunset, there is still plenty of time to enjoy the starry sky.