We do astronomy during the night. Can we do it the day? Yes, in a sense.
Because the sun hides stars' light, we can't see stars, but some heavenly bodies pierce the sun rays.
What to observe the day?Edit
Only planets, the moon and the Sun can be observed the day with the naked eye. When?
At a moment of the month, the Moon rises during the day.
Venus, Mercury and maybe Mars and Saturn are visible at a moment of the year at the sunset/sunrise, and Jupiter which can be observed also during the night.
Never see the sun directly. Use material for indirect observation, or don't observe it at all.