I understand that conductors allow electron flow because their valence electrons are 'free' to move around.. But what exactly determines this 'freeness' and the lack thereof that separates conductors from insulators?
The Hubbard model explains this with two parameters. The on-site repulsion $U$ accounts for the electron tendency to stay away from doubly occupying an atomic crystal site. The nearest neighbour hopping parameter $t$ describes the tendency of electrons to spread out or hop from site to site. If $U$ dominates an insulator results with localised electrons (or holes) . If $t$ is large enough and/or the number of neighbours is high the carriers delocalise and a metal results. Note that this model makes no assumptions about crystal symmetry or band filling.
In physics, a metal is a chemical element, a molecule or an alloy that conducts current and head relatively well. These two properties are based on the mobility of electrons that can move between atoms within metals.
We usually assess these properties at room temperatures and normal pressure. Under high pressure and low temperature most of atoms and molecules convert to conductors. So metallic hydrogen was predicted in 1935.
Only the noble gases with their stable electron configurations do not form a crystal lattice even under extreme conditions and thus the possibility of the common use of electrons on this basis is not given.
Nevertheless, noble gases can also conduct electricity. Gas-discharge lamps filled with pure argon provide lilac/violet light; with argon and some mercury, blue light. Argon is also used for blue and green argon-ion lasers.