Nefermandias
Hero
Those are the travel rules presented in the DMG.I've always found Exploration difficult to pull off. It feels a lot like scene-setting and, because of the way 5e deals with healing, it's difficult to make 'obstacles' meaningful. (you fall off a cliff, take damage. Long rest, you're cured).
But, recently, I've been playing Descent into Averness and the DM is doing a superb job of making exploration intense and meaningful. Apparently, he's using the 5e One Ring rules?
Our exploration into the fallen city of Elturel goes something like this:
DM: So, you have a mission at the graveyard and must descend from the escarpment fortress into the city. What route are you taking? How are you proceeding (directly, stealthily, main thoroughfares? etc..)
We describe our goals and our route. Based on that, we make rolls. Example: Perception for the Lookout, Stealth for the Scout(if we're trying to be inconspicuous) and some kind of skill check to Navigate (especially if we are trying to take back alleyways and circuitous routes.) This could be a History check ("I used to live here") or a Survival Check (Looking for safe ways and keeping to a consistent direction)
Depending on how we do, we can have partial or full success or complete failure. Failed stealth check means we spotted the horde of zombies blocking our way, but sadly, they've seen us. A failed navigation check could be we get turned around and take longer and darkness falls, or the people we're running from catch up. Etc..
Spells and resources make checks easier or auto-succeed. (featherfalling down the cliff allows us to bypass a blockade along the road so no need for a stealth check)
Encounters from checks (failed or successful) add interesting story bits, failures create tension and force the group to push quicker than we are comfortable or, sometimes, lead to combat and drain precious resources.
He's made it so that every foray into the more dangerous parts of the city is harrowing.
Seriously people, you should give the DMG a chance...