How bright would it be on the "face" of Titan If you were planing a maned mission to Titan and wanted to find a landing site that would get the most visible light for the longest amount of time, your first logical choice would be the dark side of the moon since it faces the sun for a longer duration than the face would. ("face" and "dark side" corresponding to the colloquial definitions they have when referring to our moon) Also, unlike the on the face, you wouldn't have to worry about Saturn eclipsing the sun. This would put you in a range of brightness roughly equivalent of twilight on Earth due to the distance of the sun and the thick atmosphere of Titan. 

But how bright would Saturn be when reflected on the face of Titan? Would it be bright enough to see anything if you wanted to go there, or would you need flashlights and night vision goggles?
It's not hard to calculated brightness to distance, but that doesn't take into account cloud cover, which is important for Titan.

Just looking at distance first, Titan (based on Saturn's distance) averages 9.6 AU from the sun, or about 1/91st as bright as the sun appears from Earth, assuming equal atmospheres.  1/91st isn't a bright sunny day, but it's probably bright enough to read by.    The sun has an apparent magnitude of about -26.7 from Earth.   91 times less bright works out to -21.8 from Titan.

Saturn is a little more tricky because from Earth, we often see Saturn's rings but from Titan, you mostly don't.   Titan orbits almost entirely in line with Saturn's rings (just 0.34854° inclination), which would make the rings appear like a thin band.   Visible but probably not very reflective.    You could also probably see ring shade and ring shine reflecting off the surface of Saturn from Titan.

How bright would Saturn be?

From Earth, Saturn's brightness varies from (mostly) between 0 and 1 apparent magnitude.  That's a range of 2.5 depending on distance and angle, which is kind of a lot.    Titan would probably receive less variation due to no ring reflection (see Saturn as viewed from Earth).

 

There would still be variation based on the angle of the sun reflecting off Saturn's surface.   Perhaps an estimate of between 0.2 and 1 is in the ballpark (as a guess) at Earth distance but Titan's viewpoint, almost entirely above the ring.

Using an an average distance between Earth and Titan of about 9.6 AU, and Titan's distance from Saturn, about 1/122 of 1 AU.  Titan is some 1170 times closer to Saturn than the Earth on average, which makes Saturn about 1.38 million times brighter from Titan than from the Earth.   which works out to between 15.3 and 15.4 apparent magnitude units.

Using my rough estimate, Saturn, from Titan would be in the range of -15.2 to -14.3 apparent magnitude, which would be some 400-800 times less bright than the Sun from Titan (it's not possible for a planet to outshine a star from the point of view of the moon), but several times brighter than the full moon from Earth.   You could probably see, well enough on Titan under a "full Saturn" - being some 5-10 times as bright as the full moon (peak -12.9/average -12.6).  It would also be much larger, so it wouldn't appear bright in the sky, but it would provide enough light to see well enough, but maybe not enough light for reading.   Enough to see though.  

Permanent Clouds

The numbers above, however, doesn't take into account Titan's cloud cover and it has nearly constant clouds.   Here is an article with a picture of a rare situation of sunlight reflecting off the surface of titan.   Mostly it's under a permanent haze.   I don't know how effective that haze is in blocking sunlight, maybe 90%, maybe even 99%, but it would certainly block a fair percentage, so, while you could probably see under sunlight, I think reading is no longer possible under those clouds.

Here's an interesting article that says Titan is brightest at twilight, not daylight, because it's atmosphere is very effective at scattering light.   It's atmosphere is thicker and much higher than Earths, and also more massive overall.     It's likely for any real work, Astronauts would probably want a permanent artificial light source and not rely much on light from the tiny sun though all those clouds.    But they might be able to see well enough to move around and explore without flashlights a little bit, but flashlights would help.

Night vision goggles would do nothing.   They see heat or longer wavelength IR light outside the visible wavelengths.   They could spot heat sources, like other astronauts, or a rip in a space suit or hut - so they'd have uses seeing where the heat is escaping for example, but they wouldn't help you see the on surface of Titan.   

Titan takes nearly 16 days to orbit Saturn anyway, and nobody would want to put up with 8 days of darkness.  Artificial light would be essential which, I would think, makes choosing a location based on sunlight not a key factor.  Perhaps someplace where there's less methane rain would be a priority, or less chance of solid ground becoming liquid under a warm spell like a nice "dry" water ice Island.