Watch out for the moon and let your eyes adjust
The moon will be a small inconvenience to see meteors tonight, but it should not ruin the screen. If you can, just take a barn or rocks or a mountain between you and the moon, so that its light does not stand out.
Remember your eyes take up to 20 minutes to really adjust in the dark, so give yourself time. Meteors often come in bursts, so do not give up if you have not seen anything after five minutes. They will come!
Also, do not be tempted to look at your phone after you are in position, every time you look at it, your eyes will take time to adjust again in the dark and you can miss the weakest meteors.