There should be a bulletin board in each guild where people can post where they are currently looking for groups, who to contact, and the type of players they are looking for. We can also sort them by most recent. Something like:

LOOKING FOR GROUP
Camp Bloodshore
R21-25 (All Classes)
Contact : Uriah Nool for invite
Posted 36 minutes ago

This would be in the Limsa Lominsa adventure guild, and people could come by and browse any groups currently underway in the region. This could also be an option whenever someone has a group to advertise it from any location, and it would go to the local bulletin board. There will also be a time limit to specify, such as expires in 30 minutes, 1 hour, 2 hours, etc. A message saying to the party leader that the invite will expire if not renewed would be cool too.

I think finding a group, even of random strangers, is by far more enjoyable than wandering around at a slow time hoping to run into someone doing something.