I live in a crappy area with no cows, sheep, villages, or anything else particularly useful. Problem is, I've been based there for a while. I have two houses (one with a mine shaft underneath it) and have chests filled with precious items. In addition, I have no idea where I'm planning on going. What's the best way for me to pack up and leave?
Depends on what you consider precious. Stone, wood, dirt etc can be found anywhere.
You can put all your rare stuff (such as diamonds, gold, etc) into a Ender Chest.
The Ender Chest allows you to teleport your items to wherever you build another ender chest (or just recycle the same one, read the wiki for restrictions on this).
With your stuff safely in a chest, you can explore freely without fear of death. Just keep a bed in your inventory to update your spawn location periodically.
I would suggest that you condense everything you have into the 'tightest' form, for instance you can turn 9 pieces of coal into a block of coal (this answer has a great summary of which you can do this for).
This leaves you with an effectively much greater carrying capacity than if you took the uncondensed components. You can also reduce the amount you need to carry by leaving a 'survival stash' in your old home, just in case you find yourself back there.
You can then put things you want to transport but not have with you into an Ender Chest (if you can't make your own Eyes of Ender, they can be traded from villagers if you have one nearby).
If you really can't get hold of the materials for an Ender Chest you could leave your most precious materials behind while you scout ahead, constructing gradual forward bases, so when you do come to transport the valuables, you can walk a distance during the day and then hide out during the night and sleep, gradually making your spawn closer and closer to your eventual destination, wherever that may be.
A more dangerous but faster way to travel is via the Nether, where 1 meter is equivalent to 8 meters in the Overworld. There's a good Portal Calculator for if you've found a spot and want to sync up portals correctly. There's some good detail on the Minecraft Wiki detailing some Nether survival techniques.
There are also some good answers on the question What is the fastest way to travel long distances in Minecraft?
If you got an excessive amount of iron and gold from your mine maybe do this: