The theoretical limit is "to the edge of the Hubble horizon, as long as you don't mind it being a one way trip." As you approach 'c' time dilation shrinks time

The theoretical limit is "to the edge of the Hubble horizon, as long as you don't mind it being a one way trip." As you approach 'c' time dilation shrinks time for you. Keep accelerating and eventually a million years outside your reference frame is mere days or hours inside the spacecraft. You could travel to the Andromeda galaxy or beyond as long as you were okay never returning to Earth or returning to a different geological epoch than the one you left. Go far enough and the sun might be in its red giant phase when you get back. You may have aged a few years or decades. This of course requires stupid amounts of energy and theoretical near maximum specific impulse, what I once heard called a "physicists' nightmare propulsion system." Something like a "photon rocket" or a relativistic velocity ion drive (propellant exit velocity near 'c') plus a very efficient fusion or antimatter reactor might be able to get you there. It was called a physicists' nightmare because if containment fails you become a flash of gamma rays in less than a nanosecond. One of my favorite wild speculations is that hypervelocity massive particles like the "OMG particle" are the jet wash from someone's engine.