Where in Universe does time move faster than it moves on Earth? I know that around black holes and areas with dense gravitational fields, time is supposed to move a lot slower, meaning that for example, a year in Earth might be just a second around a Black Hole. 
Is there a place where the gravitational field is so low (perhaps there is an anti-gravitational field), that a second of Earth might seem like an entire year there? In other words, is it possible that time would move a lot faster there than it moves on Earth?
 A: See the wiki article on time measured at GPS satellites. It's at http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
To have time go slower just climb up the earth's gravitational well. Go up to the GPS satellite orbits and general relativity has it that time will go faster, I.e., the GPS clocks go faster than the ones at the earth. It is a small effect, 45 microseconds per day difference. Actually, because the satellites are moving with respect to us, Special Relativity says time is slower by 7 microseconds per day. Subtract the two and the bottom line effect is 45-7 = 38 microseconds per day faster than clock on earth. Yes, austronauts, if high enough, age more than we do on earth. The GPS system adjusts the time to take this into account and give us time on earth. 
Go further out, not towards the Sun, and it'll be a bit faster. But not that much more, another small effect. 
The effects are pretty small, our gravity is just not much, from a relativistic or cosmological point of view. Or even including the Sun, where we are. There are some large regions of the universe with (for maybe random reasons or maybe not yet clear reasons) a lower density of matter, by more than is expected. Called voids or supervoids. Gravity will be less there, and time will tick faster also. Still by a small amount, nothing big.  
A: I think basically, the concept is that greater is gravity, slower is the flow of time near it. Earth is in the gravitational field of many celestial bodies, the primary contributor being the sun. Perhaps, if we can find a similar solar system somewhere in the universe, with a sun having lower gravitational field, time will flow faster there compared to us. It will be fastest(compared to our time measurement) where there is no curvature in space. (I don't know where in the universe such a place can be!). 
A: The surface of Pluto is a good example.  Pluto is smaller, so even if it had the same density as Earth (which it doesn't) the gravitational potential would not be as negative.  The sun is also further away, so the gravitational potential from the sun is less negative.  The surface of any main belt asteroid is another good example.
