Dragon Aerie
Your first objective at Dragon Aerie should be to light the Dragon Aerie bonfire. Find the Emerald Herald standing near a cliff. Exhaust her dialogue to receive the Aged Feather, an item that acts as an infinite use Homeward Bone. The Aged Feather is also an item that will be used to advance Navlaan's quest line.
47. Dragon Aerie, Dark Souls II: SotFS
Your next objective is to climb the ladder near the bonfire, descend along a zip line, cross a bridge to the Dragon Shrine bonfire, and light the bonfire. There's a good reason for lighting the Dragon Shrine bonfire as soon as possible. When you explore Dragon Aerie, you might inadvertently break a number of dragon eggs, which in turn can cause some of the dragons to swoop down and break the bridge near the Dragon Shrine bonfire. If you happen to be crossing the bridge, a broken bridge would mean certain death. Light the Dragon Shrine bonfire as soon as possible and then explore Dragon Aerie, breaking as many eggs as you want.
Dragon Aerie has no bosses, but it has three Guardian Dragon mini-bosses. The area has various types of upgrade materials dropped by Crystal Lizard x 11. Defeat the Guardian Dragon x 3 first, then kill the Crystal Lizards for the loots. Be wary of Undead Citizens who explode and cause your weapons, armour pieces, and rings to rapidly degrade. Stock up on Repair Powder in preparation for exploring Dragon Aerie.
You require a Fragrant Branch of Yore to unpetrify an enemy who stands at one end of a bridge and blocks a path to one of three Guardian Dragons in the area. Each of the Guardian Dragon x 3 can be safely sniped from a distance. Clear the nearby enemies first before you start to snipe a Guardian Dragon. Near the petrified enemy is another bridge that is guarded by an Undead Citizen. Crossing that other bridge would cause Fencer Sharron to invade you. The only advantage to crossing the other bridge is that it would allow you to preempt an ambush by various Undead Citizens.
Dragon Aerie is the best place for farming Pharros' Lockstone and Elizabeth Mushroom. One Lockstone is found on a corpse, located on a ledge that is accessible by dropping down from above. Be wary of a nearby Undead Citizen who is waiting to ambush you. Grab the Bonfire Ascetic near the Dragon Aerie bonfire and the nearby Elizabeth Mushroom x 3, find and collect the Pharros' Lockstone, and use the Aged Feather to return to the Dragon Aerie bonfire. Burn a Bonfire Ascetic. Rinse and repeat. This method also provides a way to farm upgrade materials from the Crystal Lizard x 11.