Another source of exp I don't think folks have mentioned yet:

When you log out for the day, be sure to do so in a Sanctuary (any town with an Aethercite is a sanctuary; you can tell you're in one by the little crescent moon icon that appears in your HUD).

Time spent in a sanctuary gradually builds up a 50% exp bonus, whether you're logged in or not. The longer you're in the sanctuary, the longer the exp bonus will last (up to a limit, but I'm not sure what that limit is).

It's not a tremendous source of exp, but every bit helps. Make an effort to never log out unless you're in a sanctuary.