It depends on what level you are. The beginning quests ask you to teleport to West City (I think there is a marker for this though), check your mail, duel someone, do a ranked battle, open your personnel shop, create a mix item (the ingredients are given to you from the previous quest), that's all I can remember right now.
Other then that, you might need to go into a dungeon, depending on your level
1 - use scanner in a monster
2 - use scanner to scan for quests
3 - use a popo stone
4 - send a mail
5 - create a party
6 - start a duel
7 - upgrade a gear
8 - fight in a ranked battle
9 - use the milleage you just got
10 - reveal a "?" item
11 - craft a mix item
12 - open a personal shop
13 - use teleport
not necessarily in that order. Its quite easy to find out what the npcs want you to do. if they give u a upgrade stone, then you should upgrade something, if they give you a "?" and etc...