It depends. There is something called whitewholes, but it is not white. A whitewhole is like a black whole but the difference is that a black whole tips a whole though time and space and kills you...
Lets label your assumptions i) Time = Space, ii) I travel through time into space. Then by symmetry of equality we can deduce from i): Space = Time, which answers your question.
Because "clock time" on Earth depends upon the rotation of the planet, vehicles in space technically have no "time of day" to reference. Those orbiting Earth might be over a particular time zone for...