If we count Avogadro's Number of stars that are closest to Earth, how big that space would be? I think that the answer to this question will be useful as a scale to appreciate the size of the universe.

So, If we count Avogadro's Number of stars that are closest to Earth, how big that space would be? And how many galaxies/clusters will be engulfed in that space? And for a start, let's just consider only three dimensions.
It's going to be all (or perhaps nearly all) of the observable Universe. Roughly speaking, there are several hundred billion stars in the Milky Way. And extrapolating the number of galaxies in deep Hubble images suggests something like a hundred billion galaxies in the observable Universe.  Put these together and you get about $10^{22}$ to $10^{24}$ stars in the observable Universe.  Avogadro's number is $6.022\times 10^{23}$, which is in the upper end of that range.  So, given current estimates, you'd need at least most, if not all, of the observable Universe to get $N_A$ stars.