1-70 is pretty grind-tastic. Northrend is considerably more fun than that, but still involving a fair amount of grinding. 80s exist only to grind themselves to a state where they can demolish anything in their way within 1-3 attacks/spells. Depending on personal inclination, however, you might enjoy leveling while going through storyline chain quests, although dungeons are easily the fastest way to level. This became so much more true after the randomized LFG made its debut.
But I think I'm rambling, so I'll summarize: It is indeed quite grindy, but not as bad as people say. If someone is willing to run you through dungeons, such as your friend, you can skip plenty of the currently-boring vanilla zones. Most of BC, too, if said friend is really good, or brings along a few others.