There's a new search feature added this recent patch that you can use to find a group. It's "Search" in the main menu. Select the area with your name to set your Seek Party status. You can also try finding other members that way.

At your level range, I'd suggest checking out the Shposhae dungeon outside of Limsa Lominsa. There's treasure chests you can hunt for free gear and gil and a ton of enemies that you can kill.