Can we define a sphere around us that would contain a star in any direction? Can we find a radius R so that in any direction around us (earth), in straight line, we can find at least one star at a distance shorter than R ?
If so, do we have an estimate ?
Or do we know that the universe density is -already- too low ?
 A: I assume what you mean is, out to what radius would we have to go in order for every sightline to intercept a star? Otherwise there is no sensible definition of "direction".
There are about $10^{22}$ stars in the observable universe out to a comoving radius of order 40 billion light years (give or take, and using the comoving radius of the observable universe) because the first stars took a little while to form.
If we assume a homogeneous universe (it isn't in time, but I'll let that slide), the stellar density is $n=4\times 10^{-11}$ per cubic light year. The mean free path before a sightline hits a star is $\sim (n\sigma)^{-1}$, where $\sigma$ is the average cross-sectional area of a star. Let's make all stars the same size as the Sun (a small fraction are much larger, but most are about half the size), then $\sigma \sim 1.5\times 10^{18}$ m$^2$.
Thus the mean free path before a sightline intersects a star is $\sim 10^{24}$ light years.
Could our local "density enhancement" (aka the Galaxy) play any role. Well the local stellar density is much higher at 0.004 per cubic light year. This gives a "local mean free path" of a mere $\sim 10^{16}$ light years.
So the answer is no, and you would need a much older universe to allow you to "see" stars $10^{24}$ light years away.
Note here that I have had to choose a definition of what is meant by radius and I have chosen the comoving radius.
