IIRC you have to talk to the balloon manager to get your ticket first.  If you don't have the proper quest or you lost your ticket, use a black stone to get a new ticket.  If you already have quest credit because you D/Ced or got off the balloon you have to walk on foot to Grana to complete the quest.

I don't understand all these steps why?

I mean, can't you create missions that you activate in the normal way?

And where I find this, I have no ea where the grit is or where the balloon is ... or from which blackstone to process the ticket .-.

edit:

The ticket was next to it, it's true you just had to exchange it with the blackstones, but they could have made it easier ..

In my opinion there is a bug, because he exchanges the ticket, and nothing happens, so if I keep it always the same ..

This particular quest is teaching people how to use the Hot Air Balloon.  A service that I have used maybe a dozen times since it was added 2 years ago.

I ask you a different question then ... what should I do to improve the character in general? In addition to the main quest

I ask you a different question then ... what should I do to improve the character in general? In addition to the main quest

Whoa! That is a long laundry list.  There are so many areas you can improve any character.  The main quests also called the Black Spirit quests will level and tell you the story about various people and ruling bodies of the land.  Gear score AP and DP will greatly improve any character to withstand combat, while gathering skill points will make your character better in battle.  Meanwhile there are all the life skills you can master up to Guru ranking.  This March I will have been playing for a year, I currently have 7 characters at level 58, and I still haven't fully explored beyond Velincia.  Games like this are meant to last a long time.  

About the balloon, I did get a free ticket during the summer event, but only to travel there.  I took the ride from Calpheon to Altinova and I think it is seriously over priced.  If you want a nice slow trip, you can board a water taxi (big ship) at Port Epheria and it will take you to Altinova for free.  Just wait for it by the dock, when it arrives board and in a few minutes it will sail non-stop to Altinova.  I took my fishing pole.  The trip I think was about 30 minutes long.  Don't try to board with your horse, they tend to fall through the bottom of the boat.  The trip by water taxi to Port Ratt is a long one, roughly an hour, and it appears to be an unused future expansion. 

Another relaxing activity is exploring the map.  I hunt, collect, and explore.  These activities might not level your character, but they will give you more knowledge about the game.  If you press "O" to bring up your quest log, the tab on Suggested Quests are optional but often profitable to your character.