Gravitational boundness is a tricky question. It's essentially asking, "will these two objects come together at any point in the future?" However, we can give approximate answers.
If there were no dark energy, then a spherical region that is denser than the critical density $3H^2/(8\pi G)$, where $H$ is the Hubble rate (equal to about $68~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ today), can be said to be bound, since it will eventually collapse. From this you can estimate the radius $r$ of the "bound sphere" that surrounds a mass $M$ under the approximation that this mass dominates over its surroundings: it satisfies $M/(4\pi r^3/3)=3H^2/(8\pi G)$.
However, there is dark energy in our universe, which makes the calculation trickier. In general, to answer the question of whether an expanding region is bound in the presence of dark energy, we need to do numerical integrations. However, we can straightforwardly estimate the maximum radius of a bound static (not expanding) region by noting that its matter density must be at least twice the dark energy density. The second Friedmann equation tells us that "matter density is twice the dark energy density" is precisely the criterion under which matter's attraction counteracts dark energy's repulsion (and this was the tuning required for Einstein's static universe model). This means the largest possible bound system of mass $M$ has radius $r$ satisfying $M/(4\pi r^3/3)=2\rho_\Lambda$, where $\rho_\Lambda\simeq 88~\mathrm{M}_\odot\mathrm{kpc}^{-3}$ is the (constant) dark energy density. That is,
$$r=[3M/(8\pi\rho_\Lambda)]^{1/3}\simeq 0.11~\mathrm{kpc}\left(\frac{M}{1~\mathrm{M}_\odot}\right)^{1/3}$$
represents the maximum radius of a bound spherical region of mass $M$.
For example, if we plug in the mass of the Milky Way and its dark matter halo, $10^{12}~\mathrm{M}_\odot$, then $r=1.1~\mathrm{Mpc}$. Note that this neglects all of the other mass that lies within $r$ (including the larger Andromeda galaxy), so the actual "maximum bound radius" around the Milky Way is somewhat larger than this. Nevertheless, the interpretation here is that in the distant future (assuming dark energy sticks around), we will retain a bound system a little over $1~\mathrm{Mpc}$ in radius, while everything else in the universe will recede indefinitely.
