Finding the nearest neighbour, from an atom within a crystal
I don't use VESTA and there are probably a few tools that can do this.

My suggestion would be to use the open source Python package ASE or "Atomic Simulation Environment." developed in part by the group of Karsten W. Jacobsen.

There are several algorithms available for generating neighbor lists and iterating through them:
https://wiki.fysik.dtu.dk/ase/ase/neighborlist.html

Here's an example from the documentation:

# get neighbors of atom 42
indices, offsets = nl.get_neighbors(42)
for i, offset in zip(indices, offsets):
    print(atoms.positions[i] + dot(offset, atoms.get_cell()))