Get rid of the hud: no more markers to follow!
I was a lot like this when I started. I came from linear shooters and I played Morrowind the same way in the beginning. It took me a few years to shake that off. My style of play is much more spontaneous now. I can't even play linear games anymore.
I use a mod that turn off quest markers. So those don't affect me. Also, I (almost) never use my map. The only time I look at my map is when I need to locate a randomly-placed quest giver.
Not to drop the M-bomb, but Morrowind's faction advancement system limits you from doing exactly what you (and I) do in Skyrim. If you're not fit for an advancement (either you're too weak or you haven't performed enough duties) you have to improve yourself or do more duties for your guild. This kind of forces other things on you. I wonder if http://www.nexusmods.com/skyrim/mods/22650/?would help you break out of sticking to a faction until it's complete.
Also do not place a check mark on quests in the journal. ON the PC there is at least one mod that disables quest markers.
I try not even to use the built in map and most games I use now a paper map. Also the clairvoyant skill is somewhat useful for finding your path if you are not using the map and the quest is dependent on the quest marker to finish it.
I tend to start with, a sort of, essential set of accomplishments.. For example, my PC is a vampire hunter so I gotta finish the Dawnguard stuff - or my PC is a thief so I gotta do the Thieve's Guild stuff. Usually, somewhere along the way this includes getting a house (vanilla houses and/or Hearthfire). By the time I finish all this, it feels natural to start exploring the wilderness around known locations and clearing out caves, bandit forts etc.
Just wandering around and adventuring is a lot of fun and definitely fits the 'open world' environment of Skyrim.
I had long ago turned off the compass and quest pointers in the HUD (as I did in Oblivion as well). The markers only show up on the map, due to the fact that otherwise, Skyrim's quests are so sparse in dialogue and Journal notes it would be hard or nigh impossible to find some quest locations without the map. In fact, unless I get hurt, or use Magicka or Stamina, I have nothing on my screen except the game world visuals.
I find it more immersive to play like this, and it encourages exploration and visual enjoyment of the beautiful game world, just following the roads or landscape cues to find things, rather than spend my exploration with eyes glued to the right hand corner or top of the screen.
What's funny is I came back to Skyrim around 1-2 years after a Steam glitch had kindly caused Skyrim to be uninstalled, and I was kind of shocked to see that Skyrim's HUD was so minimalistic and my graphics settings were set so nice... it took me a minute or two to realize that even though Steam had completely removed the game, my SkyrimPrefs.ini (set to Read-Only) was still the way I had it tweaked from my former playthrough.
Eh, don't worry about it. Everyone plays a bit different. My 2nd, 3rd and 4th characters followed the questlines, nothing much else. Then I got the bright idea, that I wouldn't go into ruins, Nordic or Dwemer unless it was quest related. ( 1st was a Jack of all trades and did a bit of everything) Which is why, I still have not been in every ruin, cave, fort or hole in the ground.
When I set up my 1st "hunter/explorer" character, the HUD went off, her RP said, smithing only leather and hide ( temper steel ), alchemy, 1h, archery and conjure familar ( wolf only). She was not allowed in walled towns or Dwemer/Nordic ruins... my choice and it was a blast. When I do a "hunter/explorer" they get an area, the first was The Rift and Falkreath Hold and that is the general area they stay in. I have basically used no or a very minimal HUD ever since ( on 360 that meant a very faint HUD or none, on pc I choose what I want to see with a mod)