With the help of BuddyPress Group Calendar plugin, you can set custom calendars for different groups and can send out RSVPs to the members. You can even provide forums for each such events. An email will be sent automatically to all the members who are going to attend the event. It also has support for Google Maps for accurate location. Overall it has complete calendar system for your website.
This is the EXACT same plugin as distributed by the developer on WPMU DEV. The developers’ links are provided above.