Let me start by saying my main Char is a Cleric so my experience is different from yours. However, I do have a low level Warrior that is now 22. With my Cleric I did a couple of quests that mostly gives faction and a little bit of coin.
Crushbone Belt Quest gives you faction with Kalidim, coin and old armor pieces that even if you can't use them, sell to merchants for more coin.
Delivering the Mail - again - you get faction small amount of coin and something like a potion which is no drop but provides for the equivalent of a spell which as a Warrior you would have no access to.
The Hallas Warriors Guildmaster or Weapons Master gives out a cute little quest delivering a drink to guards - again, good faction, a little coin, an occasional trinket to sell.
I can only really rate these as a cleric - I didn't die doing them -- so as a Warrior you would probably have it even easier, and since you are anon I can't tell where you might need faction upgrade - but you could definetly make a few plats doing all of these - and if you "hunt" on the way anything you obviously have more to sell to merchants.
Anyways, hope this helps -- I really suggest looking at the Quest postings by zone, they will indicate not only the level to do them, but the likely reward - and will often have posts by those who have done them.
Cleric of Tunare