Why do some ionic compounds have some solubility in water; why do ionic compounds have high melting and boiling points?
Ionic compounds are non-molecular; they do not have molecular boundaries. In the solid-state, each particle, each ion, is bound electrostatically to every other counterion in the lattice, and repelled by every ion of the same charge. If you sum all these attractions and repulsions up (which can certainly be done quantitatively), a net attractive ionic force results, which is why the lattice sticks together.
Boiling, or dissolution, requires that these strong forces of attraction be disrupted. For sodium chloride, these intramolecular or interparticle interactons, are compensated for by the making of ion-dipole bonds when sodium chloride dissolves in water, and the water dipoles solvate the individual ions; we write