This question has been explored in the context of global positioning systems, which need to account for general relativity. The traditional Minkowski coordinates $(t,x,y,z)$ of flat space-time do not allow for an immediate positioning in an unknown gravitational field.
Tarantola and colleagues propose a symmetric coordinate system with four times, see Gravimetry, Relativity, and the Global Navigation Satellite Systems and this talk. If four satellite clocks – having an arbitrary space-time trajectory – broadcast their proper time – using electromagnetic signals,– then, any observer receives, at any point along his personal space-time trajectory, four times, corresponding to the four signals arriving at that space-time point. These four times, $\tau_1,\tau_2,\tau_3,\tau_4$, are, by definition, the coordinates of the space-time point.
In Using pulsars to define space-time coordinates Coll and Tarantola propose to replace the satellite clocks by pulsars, to obtain a relativistic coordinate system valid in a domain larger than our Solar system.