Rookie Quests

For exp grinding 1-10, the most recommend choice is fighting bosses in arena from the Rookie Quest giver. To reach those quests first talk to the Rookie Quest girl, then select the second option twice and the follow list will show up:
*Velocidrome in Arena.
*Velocidrome in Jungle.
*Bulldrome in Arena.
*Bulldrome in Jungle.
*Gendrome in Arena.
*Gendrome in Desert.
*Iodrome in Arena.
*Iodrome in Swamp.
*Yian Kut Ku in Arena.
*Yian Kut Ku in Jungle.
Velocidrome is probably the fastest one you can do for EXP since the starter LS (and probably most other weapons) can basiclly finish it off under a minute most of the time, but you may want to run Yian Kut Ku for practice or materials for later. Remember you can always do some of the Hunter's Quests if you get sick of these.