Here's an easy and fun way to see much of the game, do lots of side quests, kill lots of stuff, get lots of loot, learn lots of shouts, but not advance either the main quest or any faction quest:

1. Use a non-combat shout in a non-combat situation near witnesses (towns work best but it also can work outside of towns provided you aren't in combat and there are witnesses (animals and followers might count as witnesses))

2. Wait until a Courier shows up with a "Letter from a Friend"

3. Go where the note tells you to

4. Repeat from step 1

The note will take you to a random dungeon (or dragon mountaintop) with a word wall. Chances are, you haven't been to it yet, so you will have a little hike to get to it at a minimum (because you can't fast travel directly there), providing you with chances of random encounters, to find other new locations, and the like. Then you have to clear the dungeon or kill the dragon. The dungeon may even have other side quests either found inside it or is a location that a different side quest you have active is pointing you to.

The shout I use most often is Whirlwind Sprint, mainly because I tend to be overburdened with loot (stuff I stashed on my follower previously and/or because a Carry Weight potion wore off) and am crawling around the town selling it off. But others will work as well, of course.

You can do this as much or as little as you want, for a breather between non-radiant quests, or just to collect shouts and loot.

Thanks for sharing.

Meh too cheatey.

Best way to go exploring is to run around aimlessly until you see something in the distance.