There is a quest called Location, location on felicitas which can be completed right now (Visit Felicitas Town Page for more info). The town is fully unlocked at this moment. I will only display the quests which are available to complete at this moment.
NPC: Kid on the entrance
 Talk to the kid near the entrance
 Give him 5 Water Megacryst, you can find it from exploration on Wolfsgang Peak and Maranda Coast (My farming area for Ice megacryst to make a hero ring)
Reward: Star Quartz
NPC: talk to the woman on the west of Q1 Kid
 Defeat 15 Gloom Widow, You can find them on Ballen Passage.
Reward: Recipe for Wind Spear
NPC: Note inside the inn
 Check the note on the inn’s wall
 Go to Maranda Coast exploration, talk to the engineer on the 1st area.
 Find 3 airship pieces on 3 spots. Refer to the Maranda Coast map above for more info about it.
The first piece is on the southwest of the engineer. The second one is located on near the Exploration point location (H2 hidden path)
The last piece is located on the area where you can find T7 and T8 (H4 Hidden path). It’s located on the “4” of my “guide4gamers” watermark :). After finding those pieces, return to the engineer to claim the reward
Reward: Mythril Helm
NPC: Tavern Master
 Go to tavern (building on the south of the inn).
 He will ask you to deliver the grindstone
You can find the stone on the Windy Height West, see the location on the picture above.
NPC: First Girl on the area 2 of the town (north from the 1st area).
 You need to finish previous quests in order to trigger this event (the quest begin in Royal Capital Grandhselt; There’s a Scaaar-maaan
 Go to Windy Height West and then talk to the man on the (1), after that talk to the lady (2) and use the item.
 Defeat Terror Knight
The terror knight is quite hard, make sure you bring strongest party, not a “grinding” party. I believe you won’t have any problem if you bring your main party.
 Bring character with raise spell/ phoenix down
 Wind and Ice resistance is nice for this battle
 Power/Magic/Full Break
Reward: Fire Lance
NPC: Woman south of Q2 NPC (1st area of the town)
 Requirement: Talk to the woman on Town of Kolt (in front of the Weapon Shop)
 Go to the NPC location (Dilmagia), and then go back to Town of Kolt to speak with the same woman (in front of weapon shop)
 Now go to Junkyard Exploration, and talk to the man there. You can easily find the man (yellow dot on your map).
NPC: Man on the “Airship Docks” (northern area of this town, past the long stair area)
[Requirement] Reach Village of Ambel
 Talk to the NPC, and he will tell you to gather ingredients for his daughter’s wedding.
 Go to Maranda Coast, you can find the glittering spot (pretty shells) on the last area of Maranda coast. Go back to the man and then he will make you a shell earrrings.
 Go to Village of Ambel, and talk to the girl south of the farplane monument. She will give you a letter. Give it back to the NPC and the quest is finish.
Vega, it’s strong gun (+40 Atk). You can get in from Tavern, simply go to the little path on the south part of tavern.
Star Quartz, go to the inn. Head upstairs and check the spot near the bed.