There are many aspects of the game available to you only after certain levels, they may or may not be appealing to you, but at least give them a try:
1. PvP(Player-versus-Player): Even if you're on a non-PvP server, there's battlegrounds, Wintergrasp and arenas where you compete with other players, it's very different from killing computer generated monsters, I found that most people I know seemed to be enjoying battlegrounds, though not everyone likes arena or Wintergrasp.
2. Grinding: This may sound a little strange but some people like endless grinding in MMORPG, maybe it will help you relax from a long day, maybe it'll help you with your depression(works for me). This includes solo killing mobs for loot, keep mining or gathering herbs, playing with the auction house etc.
3. Dungeons: These are the challenges meant for five players together(1 tank, 1 healer and 3 dps), with the newly implemented system the game could find you a team in minutes(or seconds, depending on your role). Dungeons are more challenging than quests, but not that hard to beat generally, they offer good equipments and a fun experience. Almost every person I know enjoys dungeons.
4. Raids: These are really tough challenges for beginners, and they require 10 or 25 players to complete, to beat a raid instance, people need competitive equipments, good leadership and co-ordinations. Raids are THE de-facto end game for most players, like them or not they play raids every day or week.
5. Socializing with friends: There are people who don't really care about quests or dungeons, they just have some time to kill, they could be playing with people they know or making new friends. Most girls I know play the game in this style.
Again MMORPGs are not for everyone, they could be very time consuming and some people don't like them at all. If you have a lot of time to play I would say at least level to 80(keep in mind it could take 2-3 months for a beginner), get some epic gear from heroic dungeons and try the things I said above before you decide you like it or not.