Short answer : Don't
Rover aren't technically speaking the most time-efficient way to explore a planet. 100km is longest trip i did, and it was insanely long. What's more, as you probably noticed, the risk of accident is still always high even if you are travelling at low speed with a well designed vehicle. I may be wrong, but i doubt anyone sane ever succesfully explored the whole Mun with a rover. That would take dozens of hours.
How the average rover expedition usually ends :
The best way to explore biomes is to use a vehicle that Kerbal Space Program players commonly call a hopper. A hopper is in fact a simple lander with enough fuel to hop around a planet fitted with science collecting devices. If you have a bit of piloting skills, it is a really safer (and faster) option, though it does cost fuel.
Of course, if the target planet has a dense atmosphere allowing jet engine use, such as Laythe, then you'll probably want to use an airplane. For small planets, with low gravity such as the Mun, using a liquid fuel engine powered vehicle is the only option.
Hopping around a planet :
As a reference, here is a wiki article about Hopping around celestial bodies that provides a bit more insight about Hopping vehicles design and strategies.
So why rovers even exists if they are useless for exploration ?
- For the achievement : It is much harder to design a lander for a rover than a common lander.
- For fun : Putting a feet on a planet is something awesome, but driving around with your high tech SUV really makes you the king of this place.
- Sometimes, it can be useful to move things or kerbal around your bases.
- To cover medium-small distances without performing a fuel burn with your lander.