The distance we can travel at near-light speeds is limited by the principles of special relativity. According to the theory of special relativity, as an object with mass accelerates and approaches the speed of light, its relativistic mass increases, and the energy required to accelerate it further also increases. As an object with mass approaches the speed of light, it would require an infinite amount of energy to reach or exceed the speed of light. Therefore, it is not possible for objects with mass to travel at or faster than the speed of light.
However, even at speeds significantly below the speed of light, the effects of time dilation and length contraction come into play. As an object approaches the speed of light, time dilation causes time to appear to pass more slowly for the object relative to a stationary observer. Additionally, length contraction causes the length of the object to appear shorter in the direction of its motion as observed by a stationary observer.
These relativistic effects mean that the subjective experience of time for the travelers on a spacecraft moving at near-light speeds would be significantly different from the time experienced by observers on Earth. From the perspective of the travelers, distances may appear to be contracted, and time may pass more slowly.
In terms of how far we can travel at near-light speeds, it depends on the energy and propulsion systems available to us. With advanced technology and hypothetical propulsion methods, such as nuclear propulsion, antimatter engines, or concepts like the Alcubierre drive (a speculative idea involving space-time warping), we could potentially travel to nearby star systems within a human lifetime, even though the distances between stars are immense.
However, it's important to note that we are currently far from achieving near-light speeds in practical space travel. Our most advanced spacecraft have achieved speeds of only a small fraction of the speed of light. The challenges associated with accelerating massive objects to near-light speeds, energy requirements, and the effects of time dilation make it an enormous technological and engineering feat beyond our current capabilities.