Here is a chart of the constellation Aries and the Arietids Meteor shower

June: Arietids: This is a fairly strong meteor shower that can be up to 60 an hour but it is spread out over a period of time rougly from May 22 to July 2. The peak is usually around June 7th. So, a few days before and after June 7 is typically the best time to view this meteor shower.

I have a complete listing of Meteor showers for the year here