One of my wife’s favorite pastimes is to give me lists of things to do. Right when I have things all planned out and am ready to begin she likes to toss in a “Before you do that”, and then give me a new list of things that I should do first. Sometimes she’ll even follow-up a “Before you do that” with another “Before you do that”.
The dungeons are designed for various levels so you don’t necessarily need to visit each and every one right away, but you probably want to at least locate Blackrock Caverns and Throne of the Tides. These are the two level 80 dungeons that you can start running immediately.
Because it’s underwater, Throne of the Tides might be a little tricky to get to, especially if you don’t have the sea horse mount. The other dungeon that you might not be able to get to right away is The Stonecore which is in Deepholm. This requires you to go through the Maelstrom and I don’t know if that’s possible without questing in Hyjal or Vashj’ir (don’t quote me on that though).
The other dungeons are located in Uldum and Twilight Highlands are all pretty straightforward to find, so it might be worth the time to fly to each one.