Best way Ive seen is a mob tower. The mobs spawn on multiple floors then get pushed down to the bottom floor taking big damage. You stand there and one hit them with a simple stone sword. Free drops too.
You get xp from breeding and slaughtering animals too.
Mob spawner grinder. Just look up "Skeleton Mob Grinder" on Google. At one point I killed 60 skeletons in under a minute. With a mob spawner set up accordingly they will continuously spawn. Another good one is a Blaze grinder. They're not a one hit kill though.
The Princess is in another Castle. Punching trees gives me wood.