Pet battles, archeology and dungies. There are many more pet dailies that you can do besides the 5 mentioned, more open up with each expansion - you will get xp for the fight and the quest. Riding to new pet battles, I stop to do archy and q for dungies - I'm an altoholic too LOL and have leveled 4 toons this way from level 1 - 90 in under four days. Good Luck :)
Research instances appropriate for your level online. Running instanced content is the single most important thing you can do, at least up through level 85. Instead of focusing on questing, focus on dungeons. A quick search for “WoW dungeons by level” or similar will help you find the right instances for your level. Keep in mind too that many instances are faction specific, so make sure to check Horde or Alliance specific lists!
Fishing requires much time and does not yield much profit until its later levels. Unless you enjoy it for its own sake, avoid seriously delving into fishing until your level limit. It is not a bad idea to do a little when starting out a new character on a new server, though - the gray items you fish up sell for good money to a starter, which can help you out with your other tradeskills.
Island expeditions are very easy to complete while leveling, particularly before hitting Level 116 when your legendaries are still in effect and your secondary stats have not been squished by leveling scaling yet. Island expeditions can be completed in 5 to 10 minutes relatively reliably while also acquiring some of the pets, mounts, and Bind-on-Equip gear available. There is also one weekly quest to do one island expedition, so for slowly leveling alternative characters, be sure to complete at least one island expedition each week.
But now, the Gear Advisor starts popping up, trying to get me to put the old 360 version Ring #1 into Ring #2's slot, since iLvl 360 is better than 350. Except I can't do that, because of the "Unique-equipped" modifier. So I click "Cancel". And then the window continues to pop up after every action my character takes, over and over and over, until I get rid of the old ring by vendoring, scrapping, or destroying it.