So, if a planet is tidally locked to its parent star, yes, one side will be in constant daylight and the other in constant night.
This would, logically, lead to very high temperatures on the day side and very cold temperatures on the night side. The most habitable regions (temperature-wise) would be along the border between day and night (called the terminator), where the sun is at or close to the horizon. However, such extremes in temperature would likely lead to extreme weather patterns: as the hot, low-pressure air on the day side and cold, high-pressure air on the night side will generate incredibly strong winds flowing between the two hemispheres.
In order for a planet to become tidally locked with its parent star, it would also have to have a relatively close orbit around the star, with an orbital period (its "year") somewhere on the order of only days or weeks. In order for the planet to still be habitable so close to the star, the star must be very small and cool, something like an M-class red dwarf star.
The TRAPPIST-1 exoplanetary system is a good example of this. The seven(!) rocky planets of the system orbit very close to their star, a cool red dwarf. The fourth planet in the system, the one thought to have the highest potential for habitable conditions, has an orbital period of about 6 days.
Also, a common misconception about tidally-locked planets is that the sub-stellar continents (spot directly under the sun) would be barren deserts. A lot of studies, like this one:
actually show that the amount of precipitation will increase drastically on the daylight side. [Here are a few animated simulations from that same study:
that illustrate as much. This means that you probably won't end up with lots of deserts as much as huge rainforests. Therefore, it is likely, as you asked, that there would be large bodies of water across the daytime side. However, it is surely still possible to form some deserts on the daytime side; notice several areas in the animations where precipitation is still low. This probably has something to do with the prevailing winds and mountains and rain shadows and all of that—but I am an astronomer, after all, not a climate scientist.
A tidally-locked moon, however, is a completely different ball game. The Earth's Moon is tidally locked—it only ever shows us one hemisphere due to its synchronous rotation. But we all know that the moon goes through phases (sometimes it's full, sometimes only half is visible, sometimes a crescent, and sometimes we can't see it at all), which is due to its month-long orbit around the Earth. In other words, takes about two weeks for a single "day" to pass on the Moon, from sunrise to sunset, and then another two weeks for the sun to rise again.
But the important takeaway here is that the Moon experiences night and day just like we do, albeit on much longer timescales. An astronaut living on the moon would even watch the Earth go through similar phases to what we see looking at the moon, except that the Earth wouldn't change its position very much in the sky; it would pretty much stay in the same spot all the time. All of this is simply due to the fact the Moon is tidally locked to the Earth, not the sun.
The moons of Jupiter are also tidally locked to the planet (as most large moons tend to be), so they keep one side constantly facing Jupiter, like our moon does for us. Jupiter's Galilean orbit much faster than our moon, though; a full orbit for Europa is only about 3 and a half days, so there'd only be about 42 hours between sunrise and sunset. But during every orbit, Europa passes behind Jupiter's shadow—essentially a solar eclipse but lasting for hours. This means that there are regular periods where the entire moon experiences a pitch-black night.
Long story short, though: if you want your story to be set on a planet that experiences constant daylight, it must be set on a tidally-locked planet and not a moon. Any moon, even if it is tidally locked to the parent planet, will experience regular cycles of day and night.
But even on a tidally-locked planet, the permanent daylight side would be oppressively hot. The desert regions would be beyond inhospitable, but, thankfully, the high humidity of the rainforest regions would keep the temperatures relatively low. The coastal regions might also be similarly temperate. Regions at higher latitudes and regions near the day-night border would also have much more bearable temperatures.
Whatever life evolved on this world would have to have some sort of mechanism for enduring extreme heat—perhaps something like the long, wide ears of a desert jackrabbit that act as radiators to expel excess heat. Or perhaps they are semi-aquatic and use the oceans to stay cool. But the creative parts get to be your choice :)
Hopefully that answers your question! Let me know if you have more.