April 22nd the Lyrid Meteor Shower will be at its strongest, producing about 10-20 meteors per hour. It's one of the weaker showers that will be weakened further by a nearly full moon. You'll need to look east toward the constellation Lyra to see this shower.
May 5 brings the Eta Aquarid shower when the Earth travels through the debris of Halley's Comet. Look east during this shower and you could see 20-40 meteors per hour. The moon will be a sliver in the sky, so clouds will be the biggest obstacle between you and this light show.
Toward the end of June, we will have the June Botid shower. It is relatively weak compared to others, but 10-40 meteors could be seen in the northwest sky the early morning of June 27. The moon will be between a full and half moon during this time, so viewing may be obstructed by moonlight.
As we get closer to summer, the rest of the meteor showers of the year will be posted.