If you want to take a chance on the Lyrid Meteor Shower you should be looking this weekend. This shower is usually a quiet one but can result is spectacular displays from time to time. Earth & Sky gives viewing times as the very early hours of Sunday and Monday morning. The moon will have set by then.
The quoted Earth & Sky website has some great tips on watching for meteors. Nothing is a sure thing when it comes to Lyrid meteors, but it would be wise to take along a camera if you plan to go watching.
Source: Slashdot