…at all latitudes or is it possible that there is a region on earth where the moon is visible every day?
Could you possibly reword or add details to your question? I’ve sat here and had to read it slowly, one word at a time to even get what I think might be your question, not sure but what I think you’re asking is; is the moon consistently visible at all latitudes through-out the lunar cycle. I’m not sure what you’re asking about with the last bit about some areas where the moon would be visible everyday, that part needs clarification as it sorta throws the whole question out of whack for me.
First of all, consider the Sun during the year. In December, the Sun is directly overhead in the S hemisphere. It is visible for longer in each 24 hour period the further S you go. In the Antarctic Circle, it is perpetual day; in the Arctic Circle, it is perpetual night. In June, this is reversed. The Sun is directly overhead in the N hemisphere, and days are longer the further N you go.
The other thing you need to know is that the Moon orbits the Earth in roughly the same plane as the Earth’s orbit around the Sun (about 5 degrees difference). At new Moon the Moon is in the same direction as the Sun. With the Sun behind it, the new Moon is not illuminated, and it rises and sets at the same time as the Sun. At full Moon the Moon is opposite the Sun. It is fully illuminated, it rises in the evening and sets in the morning.
From all the above, you can work out the following.
At a new Moon in December, the Moon is in the same direction as the Sun - overhead in the S hemisphere. At a new Moon you cannot see much of the Moon because the Sun is behind the Moon, and the Moon rises and sets at the same time as the Sun. But to the extent you can see it, it is similar to the Sun - the further S you go, the longer you can see the Moon in each 24 hour period. If you go close enough to the S pole, the new Moon is visible continuously for 24 hours; if you go close enough to the N pole, the new Moon is never visible.
At a full Moon in December, the Moon is opposite the Sun - so the Moon is overhead in the N hemisphere. Thus, the visibility of a full Moon in December is similar to the visibility of the Sun in June. The further N you go, the longer you can see the Moon in each 24 hour period. Near the N pole, you can see the full Moon continuously for 24 hours; near the S pole, you cannot see the full Moon at all.
In June, all the above is reversed. So, for example, at a full Moon in June, you can see the full Moon continuously for 24 hours near the S pole; the full Moon is not visible at all near the N pole.
This website shows you what parts of the Earth can see the Moon (and the Sun) at any date and time.
I’m not questioning Riemann’s accuracy, but it might be more complicated than the OP is looking for. So, on the chance that the OP wants something simpler, I will offer this:
The earth is a 8000 miles in diameter, and the moon is about 240,000 miles away. In other words, compared to how big the earth is, the moon is VERY far away. So the moon is always going to look pretty much the same, no matter where on earth you are looking at it from.
I think he is asking if there is somewhere the moon is always lighted and never “new”? In which case, the answer is “no”.
I’m also guessing that’s what the OP is asking. But, new moons are illuminated somewhat by the Moon’s view of the day lit Earth, and I think this happens every day (though not necessarily all day). Direct sunlight isn’t the only way the moon is visible.
The question sounds like it’s multiple choice with two possible answers, but if I’m reading it correctly, both answers seem to mean “yes, every day there is some place from which you can see the moon”. In which case, the answer is, “yes”.
[This was meant as a reply to Darren_Garrison but I don’t seem to have hit the reply button there]
Thank you, that is the answer I was looking for.
If that’s what the OP was asking - of course. A new Moon or full Moon is a function of where the Moon is relative to the Sun, which changes on a monthly cycle as the Moon orbits the Earth. When it’s a new Moon, it’s a new Moon anywhere the Moon is visible on Earth. When it’s a full Moon, it’s a full Moon anywhere the Moon is visible on Earth. Which places on Earth can see the Moon and for how long is a function of the Earth’s 24-hour rotation.
I know it sounds complicated, but once you visualize what’s happening, the full picture of how long the Moon is visible at different places on Earth is simpler than it seems. If you understand the Sun during the year, and why the length of days varies due to the tilt of the Earth’s axis, then you just need to add in the knowledge that in the Moon’s monthly orbit, at new Moon it’s in the same place as the Sun, at full Moon it’s opposite the Sun.
Thus, at at a given latitude:
long summer days > new Moon visible long time, full Moon visible short time
short winter days > new Moon visible short time, full Moon visible long time
Not quite: it also depends on which side of the moon you are observing! 
I don’t really get the joke, I don’t see anything inaccurate in what I wrote. “Where” in this context obviously means “where in the sky”, i.e. “what direction”.
Yes, I do not expect my little joke killed anyone with laughter. Though, interestingly enough, the moon is close enough to have a large parallax on Earth, nearly a degree sometimes. (So two degrees for the entire diameter, which could affect precise phase timing)
The phase of the moon changes by 13 degrees per day, so the parallax effect is negligible with regard to phase.
There was an awesome pic of a barely-new moon on the Bad Astronomy site a few years back. It showed a very thin crescent-only a few pixels wide-set against a blue daytime sky.
Thank you for this post, because you have explained something I had observed with this month’s full moon just a couple of days ago.
We recently moved to a seaside cottage with a view of the Atlantic. Our back picture window looks to the northeast, and when we first arrived in June, we could see the sun rising over the ocean. As winter approached, and the sun rose further to the south, the view of sunrise was blocked by the house to our right.
But I noticed the other night that the full moon had risen almost directly out of the northeast, which surprised me, because I knew that the moon’s orbit is only about 5 degrees inclined from the ecliptic, so I naively expected it to rise close to the point on the horizon where the sun rose. When I checked timeanddate.com, I found that the sunrise and moonrise points differed by about 70 degrees. Although I studied astronomy in college (back in the days of Ptolemy) and for many years had a job adjacent to a major planetarium, I was puzzled by this and was even thinking about posting here for an explanation.
You beat me to it. Your post has nicely cleared up my confusion. Thanks!
Also, a 5º difference in plane can lead to a much greater difference in azimuth on the horizon.
Some amateur* astronomers try to get a pic of the new moon as soon after the sun-moon conjuction as they can. A conjunction is when two objects have the exact same longitude, and if one of them is the sun, then it’s impossible to see the other object at that time.** I’m not sure off-hand what the record is for the newest moon sighting, but somewhere around 13 hours. There are similar attempts to see the oldest moon, which record may be around 17 hours. But I’m going by hazy memories of things I read in Sky&Telescope, so these numbers are likely to be off.
*There’s no scientific use for these sightings, so it’s a purely amateur preoccupation.
**Not counting solar eclipses, of course.
Nobody’s mentioned this yet, so I’ll pitch this bit in: If the question were “is there a place you can go where the moon is always full?” a good answer might be the LaGrange point between the Earth and the Sun.
Looking back at the Earth and moon from this place, the lit side would always be facing you. Unfortunately this point is not on the Earth; it would require a rocket ride then a coast through space probably weeks long.
A decent picture is found here (although the discussion is more about the moon’s color than the fact that it and the Earth are “full”):
When I first saw OP’s question, the thought that occurred to me was that the question was “Is there a place on the Earth where you can always see the moon (where it never sets)?” Answer: I don’t think so, not a place you can consistently stand and get this effect, but I believe you should be able to find a place where this sometimes happens.
Near the Arctic (and Antarctic) circle during the local summer season, you may see the sun circle the horizon, not fully setting and not rising that much. There might be latitudes on the Earth where you get the same effect for the moon. However, with that 5 degree inclination offset, that’s enough so that the apparent width of the moon (half a degree) is so narrow you might not ever see it stay risen all day…or not? @Riemann?
Adding a smidge to my last post, I believe (via thought experiment) that if the moon is, for instance, currently “in the northern hemisphere” and your latitude is high enough north, then you should be able to see the moon circle the horizon and never set, some days.
There’s no scientific use for these sightings, but that’s not the same as saying there’s no professional use for them. Some traditional calendars (such as for religious purposes) are officially based on the first sighting of the new moon, and so officials of those religions might pay astronomers to make these observations.
The relevant graph is in the back of the Air Almanac. For example, on December 20 the full moon does not set above, let’s say 65N.