Water is very useful for rocket fuel and life support in space. But does water, in abundance and form which conceivably could be usefully mined this century, really exist in NEA's? Or do we have to go all the way out to the frost line, the Asteroid Belt, to find asteroids with available water? (Lunar polar water ice is not topic here, I think, but low delta-v asteroidal water).
No and yes.
I'll address the "no" answer first. The answer is no if you truly mean "water ice". Ceres is close to the limit of where water can exist as water, as opposed to in the form of hydrated rock. Those intriguing bright spots on Ceres may well be water ice that has been exposed to vacuum (but they might just be salts). Ceres most likely is inside the frost line, but just slightly. That's part of what makes Ceres so intriguing. Ceres orbits at 2.7+ AU. It is not a Near Earth Asteroid. Contrary to mainstream thinking, perhaps the current frost line is at 2.7 AU (as opposed to 5 AU). There's no way that it is at 1 AU.
The answer is yes if you look beyond ice as a source of water. Some carbonaceous asteroids contain water in the form of hydrated minerals. Some of them contain quite a bit of water, up to 22%. We'll find out more when OSIRIS-REx launches next year and returns a sample from 101955 Bennu in 2023.
Plugging numbers into the Stefan–Boltzmann law gives us a temperature near 273°K (0°centigrade) for bodies near earth's orbit. The exact answer for atmospherless bodies depends on albedo. Any water on nearby asteroids will thus boil until it freezes, and then sublimate. That's why the search for nearby ice is focused on lightless, cold regions of craters near the moon's south pole.
Space probe Rosetta and its attendant comet are still 200 million km from the sun, and already outgassing water. IIRC, that started back in January, when the comet was 390 million km from the sun, well beyond Mars. Black body temp. out there would be around -100°C.
Looks like I was wrong about when jets first appeared: More jets from Rosetta's comet! September 19, 2014. On that day, the comet was 500 million km from the sun. That's outer belt. No spectra that I know of, so possibly not water. Water seems most likely though.
Likely we'll have to go out at least that far to find ice on small bodies.