Can an astronaut tell the difference between the weightlessness she feels in orbit and the weightlessness she would feel if gravity weren't acting on her? Could you go anywhere where you would not be affected by gravity?
Yes, an astronaut can tell the difference between the weightlessness in orbit and the weightlessness if there is no gravity. In orbit, the astronaut experiences motion with the acceleration of free fall (approximately g = 9.8 m/s^2 on Earth, but the real value would depend on the radius of the orbit.) If the gravity, and presumably any other forces, are not acting on the astronaut, s/he experiences motion with the zero acceleration, or constant speed. These two motions feel differently (much like traveling in an accelerating car feels differently than traveling in a car moving with the constant speed.)
If you are in outer space the gravity acting on you will be negligible because you will be very far from other objects that can exert the force of gravity on you.