In order to help you find some direction, I've put together a list of 10 easily attainable achievements that you can earn in the next few days while questing. These are along the way, so you won't have to break your stride. Many can even be achieved today.
1. Train one of your professions! A skill of 350 in any of your professions will open up the ability to train Grand Master, which will award you with the achievement, Professional Grand Master. Check out our guide to finding your profession trainers.
2. Most level 70s will have at least two professions with a minimum skill of 350 by this point, so why not train them both to Grand Master? This will give you the achievement, Working Day and Night.
3. If you have leveled Fishing, First Aid and Cooking to at least 350, and train their Grand Master ranks, you will earn the achievement, Skills to Pay the Bills.
If you haven't, but would like to, then check out our guide to leveling Fishing to 375 as well as Cooking to 375. First Aid should be a breeze, as all you need is cloth! Still, should you find yourself at a loss, check out our Guide to Farming Cloth.
4-6. As you should know by now, there are two starter areas; Borean Tundra and Howling Fjord. If you ride around and fully explore the map of each, you will earn two achievements, Explore Borean Tundra and Explore Howling Fjord. Check out our guide to reaching each starter zone!
After that, try riding through Dragonblight. It's a level 71-74 zone, so it shouldn't prove too challenging!
7. Instead of flitting back and forth between each starter zone, choose one and settle in. If you can complete 150 quests in the area, you will be given the achievement, I've Toured the Fjord or Nothing Boring About Borean.
8-10. Everyone is going to be itching to try some of the new dungeons, so why not hop into queue? Finishing Utgarde Keep on regular mode will grant you the achievement, Utgarde Keep. You should also be able to queue The Nexus and Azjol-Nerub.
Not sure how to get started? Check out WoW Insider's Utgarde Keep Walkthrough.