While a concentrating on this spell how is the characters sight affected? While able to traverse through earth and stone how would the character know where to go or gauge distance? 

The spell doesn't grant any additional senses. Keep in mind that the spell also doesn't grant any additional movement speed and you can't end your turn within stone... so odds are even if you spend your whole turn "swimming" underground, you're still going to a location within range of sight, so it's completely within reason that your character can simply calculate where they intend to end up. The only downside is if you're trying to walk through a stone wall... in case there's some guys on the other side waiting to attack the first person they see... in that situation, you would have no way of knowing the danger until you saw it.

Yup, you have to swim blind, because Investiture of Stone does not grant any special senses. 

Does having your head underground explicitly tell you that you become Blinded? No. But:

1. We know that Total Cover and Heavily Obscured are the ordinary consequences of having a solid wall of material like earth and stone between you and whatever you're trying to look at. 
2. We know logically that light does not penetrate solid earth and stone, and we know mechanically that light is required to see, and that's its absence causes Darkness. 
3. We know logically that having your head buried underground would mean that you couldn't see anything. 

That's enough for me to tell me that you're effectively Blinded while gliding underground, even though there isn't any page in the PHB that specifically tells you what happens to your vision when you're buried alive. I'd hold that not only for creatures with normal vision, but also for Darkvision as well, since we've got more than just Darkness causing a problem. 

Generally speaking, a player will cast Investiture of Stone with a particular application in mind. It doesn't last long enough for casual exploration.

So, the player is likely to be travelling just within the wall or floor, or passing through to a known space beyond. Both of which only require straight line movement. The former allowing for "peeking" during travel. Unless heavily inebriated, an adventurer shouldn't have any trouble walking a straight line.

If worried about measuring distance, measure it in time instead. You can spend roughly 6 seconds submerged at a time. If you've walked straight into a wall for 3 seconds, it's time to turn around.

With irregular cave shapes and upward/downward slopes, I think that there's a pretty good chance you could charge forward towards the cave you think this is just on the other side of a wall, and accidentally run under/over/around it. I wouldn't make it a hard check, but there'd probably be some sort of a perception, investigation, or survival check I'd ask for to orient yourself for anything other than trivial wall hopping. 

We can try to draw conclusions about what it's supposed to be like from Meld into Stone...

While merged with the stone, you can't see what occurs outside it, and any Wisdom (Perception) checks you make to hear sounds outside it are made with disadvantage.

Seems weird they don't just say you're blinded. It almost sounds like it's saying you can see what occurs inside the stone? Obviously there would need to be more explicit wording to actually allow this mystical stonesight. Hmm, maybe we're better off not looking at how it's handled in other spells.

It does seem like there could be situations where sensing your surroundings while in stone could seem reasonable. Like would a delving dwarf be able to use IoS to dip into tunnel walls and check for ore veins? Could there be some kind of feel or taste or something to a change in rock type? I'd probably allow something like this if a player asked.