A few of these have been mentioned already, and I don't know if I'd say any was best, but:
Just Cause 2/3 - The grappling hook and wing suit are incredibly fun. The vehicles don't handle as well but the core method of traversal is so fun, engaging, and efficient this isn't as big an issue.
Gravity Rush - Not much can be said that hasn't already been stated.
Prototype - Possibly the best thing about the traversal is how incredibly quick it is. Travelling large distances never felt bothersome, and it was quite fun how quickly you could travel between areas when fully upgraded. The gliding mechanic, the speed at which you moved, the use of vehicles, the ability to easily traverse vertical environments, and the distance you could jump made it more fun than annoying to get around which really contrasted with infamous to me.
Shadow of the Colossus - Perhaps an unusual choice, but the control of the horse, and player character were enjoyable combined with the type of environment it was. The climbing mechanic is something where a lot of games struggle to balance 'fun' with 'frustrating', but here I feel it was absolutely nailed, which is essential when so much of the game revolves around being able to climb and scale large creatures quickly, and a lot of the enjoyment rests upon the climbing mechanics combined with solving the 'puzzle' of how to climb them.
Mirror's Edge - One of only two first person games I've played in which I've enjoyed traversing on foot as much as the rest of the gameplay. Not much I can say, but the fluidity with which you can move around the environment makes it very satisfying, even if the game has many flaws.
Dishonored (haven't played the second but I presume it's the same) - Possibly also an odd choice, but the combination of powers you have that let you very quickly move around the environment, combined with the fantastic level design, make moving across the world very entertaining. Not only is there Blink and the jumping mechanics, but the ability to control others, to stop time, and to survive a large fall by killing an enemy intertwine the combat mechanics and the traversal mechanics in a very satisfying way.
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Warhawk - Not one I expect to see too much in the thread so I want to really elaborate on this, and is really the reason I've posted, since it's possibly the most fun navigating a map I've had. Every single traversal method, in its own right, is an absolute blast for the maps you play on. Almost any one (excluding the tank and jeep) of them in isolation could serve as the foundation of its own game. Combining them all in a single game resulted in a huge variety of play styles which were largely well-balanced in their combat abilities (the Warhawks themselves were, in isolation, much more powerful than any other method of transportation, but with both teams having a near-equal ability in the air that advantage was lessened), and gave you a plethora of fun ways to traverse the environment.
On-Foot with a Jetpack:
First there's the Jetpack which was added in the final DLC. What separates it from many other jetpacks in games is the 'boost' mechanic. Not only can it allow you to fly into the air, or jump from air vehicles, but you can also boost very quickly in any direction which allows you to recharge. This mechanic is also used to dodge missiles, as well as to travel a great distance very quickly, so the increased movement (if you use it for that) comes at a bit of a trade-off, since usage of the jetpack allows missiles to lock onto you. Not only is it fun in a combat orientated fashion, but it was an extremely enjoyable addition that allowed those who preferred playing without a vehicle to quickly traversing around the map while being well-balanced. It's a shame it came so late, because it was very fun to allow you to go into a vehicle, travel quickly in that, and then boost away as you jump from it into the enemies base. It also added a new verticality to the ground based combat, and opened up the map further by giving troops greater places to hide. It's impossible to find a good video of the versatility and fun it adds to traversing the map (or a gif) so this is the best I can find (note: it's purposely time-stamped to skip the awful beginning):
https://youtu.be/maN6L74rnk0?t=53
On foot alone was nothing exemplary as a traversal option, as there wasn't any real variety, but when the jetpack was added it became a very enjoyable way to travel around the map.
Warhawk
While a typical air traversal option, something that separated this from other air vehicles in games were the hover mechanics, the boost mode, and the two different control systems (Pro flight, and non-Pro flight). They were really fun to just fly around in, and the various modes of flight could be combined to add further fun in getting around the map, such as by boosting, going into flight mode, and simultaneously exiting the vehicle to jump huge distances in the air.
Four-by-four (jeep)
A typical jeep, but the jeep in Warhawk was particularly fun because of the physics it was bound by in the game. Not only did it bob around with almost any change in the road making it very fun to drive, but the way it interacted with Warhawks and could be sent flying if hit by one (
https://www.youtube.com/watch?v=qyJ_ItVQ3QM) resulted in some ridiculously fun games of Capture the Flag. It also had an absolutely ridiculous ability to climb near-vertical slopes (potato quality:
https://www.youtube.com/watch?v=R7UoH8icK5g). Being a very valid combat option resulted in one of the most fun jeeps in a game.
Tank
Not a particularly noteworthy traversal option. Basically a slower jeep.
APC
This is the one I wanted to talk about the most. It was a new vehicle added in the Broken Mirror expansion pack and possibly the most enjoyable way to get around the map in the game (it is no coincidence that Broken Mirror featured one of the largest maps in the game). While in it's standard driving mode the APC is not too different from a standard jeep (with the ability to drop a bubble shield which destroys planes, to serve as a spawn point for troops, and to hold six passengers), the 'boost' mechanic of the APC (which can destroy most other vehicles) made it an incredibly versatile, fun, and sometimes ridiculous way to get around the map. The driver of the APC was able to charge it up for a certain period of time, and after the APC was charged, depending on how long it had been charged, it would rapidly shoot away and be quite difficult to steer in this time. When boosting, it could launch over jumps, up the side of mountains, bounce around terrain, and was an incredibly versatile way to travel around the map. Not only was it a very viable combat option, and resulted in some completely ridiculous situations (fighting of planes, ridiculous jumps, bizarre physics, unfortunate team deaths:
https://youtu.be/oe95uP1PDDo?t=96), but it was an absolute blast to travel most of the maps in it. If there was one vehicle which should have been in the game from launch, this was it. It was an incredibly strong addition to the game.
Dropship
Added in the Omega Dawn expansion pack, which unfortunately was the first one released. Similar to the tank, in its own right travelling around in a drop ship wasn't particularly noteworthy, but the one interesting addition it brought to the traversal mechanics was its ability to lift ground vehicles; be they tanks or jeeps. It gave tanks a new-found versatility in allowing them to be dropped in otherwise inaccessible points. The Omega Dawn expansion in itself did not seem to be too popular and the drop ship was largely unused simply because it was not strong enough to hold its own against almost any other vehicle in the game, but it was still another interesting addition to the options one had to get around the map.
