Ok, I didn't really think this was going to happen tomorrow. I've been working on this post for the last few days and adding to it as I think of new things. But since the world changes are likely going in tomorrow, I'm pushing this out for your guys to take advantage as best you can.
Change your hearth stone to a Classic city. Start acclimatizing yourself to travel without portal cities. It's not that terrible =)
Craft any items you've been planning to sell to lowbies. Post these for sale the day before Cataclysm launches so they're ready to purchase on release day.
Farm the materials you need to skill up after you unlock Illustrious rank, if you intend to use WotLK recipes for early skill points.
Purchase any Limited Supply recipes you need to power level professions on your new Goblin/Worgen before the world changes. Some vendors may be lost or confused in the mayhem.
Snatch up Limited Supply recipes from zone vendors who may be affected by the Cataclysm. Many zones are changing and these recipes could be hard to find later! This tip does not apply to vendors in the city.
Make or purchase copies of Scroll of Enchant Gloves: Gatherer for all your characters who need one. Use a pair of Herbalist's Gloves if you have a flower picker :)
Skinners: Farm Finkle's Skinner from The Beast or Zulian Slicer from ZG for less hassle while skinning.
Make all relevant crafted items for your new Goblin or Worgen and have it waiting in the bank so you don't have to waste time on launch day. This includes any glyphs and enchant scrolls they might need as well. Don't forget to give them a gathering enchant too!