[If I remember correctly] any system of mass would have it's own center of gravity. So what you could have is a ring of (evenly sized and spaced) planets rotating around an empty centerpoint. [I'm not that well versed on astrophysics so no guarantees]
From their in-system perspective each planet would be completely stationary and if the surrounding nearby universe is a homogenous nebula or somewhat devoid of stars/things nobody would be any wiser either (until the development of super-powerful telescopes, but given the lack of a starting point it's plausible for those to never be developed)
In such a system Space travel would work more or less similarily to our current solar system, except that you'd have the next planet MUCH closer by
