Is there some way I can edit the URLs that a group can visit?
When I go to Site Settings > People and Groups > Settings > View Group Permissions I can see the permissions that the group has on the URLs. But can I add/delete these URLs?
You need to go to the location where you want to change the permissions (perhaps /site/subsite). Then go to the Site Actions / Site Settings / Site Permissions. In some types of sites this route varies a little, but you should get the idea. From that interface, you can change the permissions a particular group may have on that site.
In other words, SharePoint permissions management is location-centric, not group-centric.