Some of my funnest memories in Wow are exploring the new world as a low level toon. It is much more fun doing that the first time through than sitting around at level cap. The thrill of going down the road and venturing just a bit too far, escaping from higher level monsters (or not), simply should not be skipped.
I love coming across completely new players in the game. I've often helped them by getting them a skinning knife, or giving them a ride to the mining trainer. I may make them an extra bag, and give them some advice like "Level your gathering professions and sell what you gather at the AH, and don't beg for gold." Don't throw away some of your funnest wow memories.
It's great that you have a level 80 toon. Make it the second character that you level to 81. Take a level 1 mage and get him to level 20. You will then have a better understanding of how mages work. What ever other characters you have should continue to level and see the content. Also, be aware that you can go to the bulletin board in your capital city and get a quest to go to Mount Hyjal, your other level 80 area. You don't have to level in Vashir, the underwater zone. Not everyone likes the 3d aspect of leveling underwater.
Good luck and have fun gaining experience. Don't jump in over your head right away.