You can get 3-4 per city each 36 hours.
This may not be of help to you, if you keep all classes you're interested in leveling at about the same level. I usually have a class I'm leveling at a lower level, so I pick up 7 battlecraft leves in one city: 3 from rank 20 group and 4 from the rank 10 group. I usually then pick up either a rank 1 if I have a class low enough to make use of it or if it offers something useful as a reward (that's not often, but it does happen), or a fieldcraft leve to make up the difference.
The other option is to team up with others and trade teleports, sharing levequests.
Another option to extend the number of leves you do in 36 hours, though this does not help you get the 8 leves you can get for yourself: Team up with another person or a group, you get leves first while the others wait at camp or head to camp without getting leves first, the party does your leves, then the next person in the party goes to get his/her leves. Rinse and repeat until you're out of leves. If you get as many as 3 people together, this can take quite a bit of time and result in a lot of experience gained. The group I did it with in open beta didn't have time to finish all of them before we were falling asleep. :P
You could then use the suggestions others have already made about trading teleports. I think doing those two things together (sharing one person's leves at a time and trading teleports) is the best use of your allotted leves per 36 hours. If you're wanting to just go solo, you can do what I first suggested.
FFXIV: Luthien Tinuviel, Elezen Female, Balmug (And will re-roll on a new server in August)
FFXI: Luthian, Elvaan Female, Bismarck (originally Luthien on Seraph):
85RDM | 80WAR | 76DRG
I've always been of the opinion that Warrior was the Swiss Army Knife of Vana'diel.