I am the same way. I am 38 hours (Lvl 20) in and still basically in Whiterun. i am in no rush to do the main quest, I end up splitting time between skilling up and doing zones/dungeons. I don't know about how others handle dungeons, but I take the Indiana Jones approach. Explore, search, etc..
It depends.
With my brainless orc, I just charge blindly brandishing my axe and killing everything that moves. Then I ask questions.
If I go with my wood elf assassin, I move in the shadows and kill my targets methodically, with maximum precision and minimum effort. Then I hide their corpses.
If I go with my mage, I have to investigate the artifacts, read the books, study the history, the architecture and the life forms that inhabit the place. Then I take all the books and interesting artifacts home, where the biggest library and the most powerful artifacts of Skyrim lie.