Tuesday morning will be the peak of the Perseid meteor shower. This is one of the best know meteor showers since its a very dependable performer (averaging over 60 meteors per hour). The timing is also good. Occurring in summer with warm weather and people out late its a great introduction to watching meteor showers.
This year the moon is 80% of full on Monday night/Tuesday morning. Your best strategy is to take a nap until 2:00am Tuesday morning and start observing then. At that time the moon will have set and the sky will be dark.
Sure you can stay up all night and you’ll likely see several bright meteors per hour but you’ll miss seeing the fainter ones in the moon light. My personal experience is that observing a meteor shower under the full moon is less than exciting. The darkness of night sprinkled with shooting stars is the magic that draws me to out.
With this years moon light I have no plans to travel to a dark site. That and the weather forecast does not look good for Tuesday morning here in eastern Kansas. So I’ll observe from my rural site and hope for some clear skies!