Groups would probably be better referred to as Campaigns.

When you log in, you should see a list of campaigns of which you are a member. Current options are only "Groups" and the list of New Groups.

Move the Calendar up on the page.

On a campaign page, either near the top left or the top right, a list of subpages, eg. Characters, Maps, Blogs/Notes, etc.

A specific Campaign Notes page to be written up by the admin, separate from character blogs.

User aliases, so users can have a name in a specific campaign.

Simplify the interface, removing as much as possible. There's a lot of Drupalisms that serve only to confuse.