leveling another job on same character

If I decide I want to level a different job on my same character (rather than rolling an alt), what's the best way to gain XP? Since I'll have done the quests up to my current level from my starting city, I assume they're not all magically available to repeat. Is there a different starting city I can relatively easy get to? Or is there a better way to level the new class/job? Also, I notice that once I hit level 10 I get to spend attribute points...will the new class also get the same number of points to spend once hitting level 10 or is it just a finite amount?

You get an xp buff on all classes except your highest that helps to offset the lack of quests. This xp buff effects xp from mobs killed and IIRC fates. Best bet is dungeons after you get to level 15. Also starter quests are all available in each of the 3 city states that should help you get to at least level 10. If you started in Gridania you can get to Uldah fairly easily, though it does require some caution in a few zones if you aren't at least level 30 already as there are some higher level mobs that can 1 shot low level players if you don't pay attention.

Every alternate class/job you play on your character gets the same number of attribute points to spend as the original class you started with.

So, for example, if you begin as conjurer and become a white mage and level that up to 50, you will have a total of 30 points to spend on things like mind, piety, etc.

Then if you decide you want to also play bard, you begin as a level 1 archer and can eventually level that up, become a bard and get to level 50. You will receive a new set of 30 attribute points to spend on your archer/bard class for dexterity.

As for leveling these alt class/jobs, I have always done a combination of Fates and dugenons as well as all of the class/job quests that you can get.

Every city has a handful of starting quests you can do that'll get you a couple levels from the start. You have Hunt Logs, FATEs and Levequests until level 10, you can do Guildhests at level 10 (not worth spamming past the initial clear/daily roulette though) and once you get to 15 you can do Dungeons and incorporate the prior methods. Once you're level 16 you'll have two dungeons available to you and will be able to do the daily low level dungeon roulette as well.