Just do the tutorial quests. There's not much to fight at this level.

Edelstein is your friend: it has fast spawn, reasonable sized maps, and monsters that'll help you 10 to 30 all in one area. It's also reasonably unpopulated.
Patrol Robot | Level: 14 | HP: 225 | MP: EXP: 24 (10 - 15)
Serpent | Level: 18 | HP: 325 | EXP: 32 (15 - 20)
Streetlight | Level: 25 | HP: 525 | EXP: 44 (20 - 25)
Baby Boulder Muncher | Level: 33 | HP: 1,200 | EXP: 72 (25 -30)
Big Boulder Muncher | Level: 35 | HP: 1,400 | EXP: 79 (28 - 35)

Or Golem Temple. (I find the spawn a little slow though)
Golems. Golems EVERYWHERE.

The Mushroom Kingdom questline is a little slow compared to "grinding", but after ~45 minutes of questing you should be about level 35.
When you get to the last tower, just keep killing the Yeti/King Pepe. It's amazing EXP from 30 to 50 and perhaps even 70.

Alternatively, you can train on Prime Minister instead. How, you ask? Simply defeat Prime Minister as you normally do, but don't complete Violetta's quest. Instead, quit the quest and accept it from Violetta again. Prime Minister will spawn again, and that's all there is to it. You can do this is the Yeti/Pepe rooms get full.

If you don't wish to farm the above, you should still be at ~level 37 after all the quests are done. From there you can move to Orbis. From 34 to 45ish you can stay in Cloud Park VI. It's a little awkwardly shaped but the spawn is wonderful. You cycle the map by going up the Z, then dropping down, clearing the floor (left to right), and then go up the Z again. Later (45 to 55) there is Stairway to the Sky I. The spawn is AMAZING. Compare the EXP to Scarecrows. Scarecrows are 220 EXP, versus a Cellion's 156. However, Stairway is almost always open AND it has a better spawn. People always underestimate that map, I don't know why.

At level 55ish you can start going to Ludibrium. Toy Trojans have a decent spawn and has a small, packed map. Not as amazing as Stairway to the Sky but still very good.

Toward your last 20 levels to 3rd job, you can start heading to Robos. The map is a little big, but the spawn is very good. If you happen to have an attack that hits two platforms, then you're going to level very quickly here.

After Robos you should move on to Omega Sector. I especially LOVE Plateon Field for its MASSIVE spawn and small map. Defeat Monsters looks just as good/better and has an excellent spawn as well, however, it takes a bit of walking to cycle. If you're a very mobile job you will excel here.

White/Gold/Grey Yeti and King Pepe | Level: 35 | HP: 70,000 | EXP: 4740 (35 to 50 - 70)
Prime Minister | Level: 38 | HP: 85,000 | EXP: 5340 (35 to 50-70)
Luster Pixie | Level: 54 | EXP: 151 (levels 44 to 50)
Cellion, Lioner, Grupin | Level: 55 | EXP: 156 (levels 45 to 50)
Toy Trojan | Level: 67 | EXP: 263 (levels 55 to 62)
Robos and Master Robos | Level: 68/69 | EXP: 274/285 (58 to 63)
Plateon | Level: 74 | EXP: 382 (levels 64 to 70)
Mecateon and MT-09 | Level: 75/76 | EXP: 403/446 (levels 65 to 70)