G shift to H

I've been a silent passenger on this e-group for a while, but I'll now take
the plunge and pose a question.

The example that puzzled me arose with Slavonic languages. I notice a
consonant shift from g to h happening (or perhaps the reverse - I don't know
which came first).

Example (one of many): Russian/Polish grad / gorod and Czech / Ukrainian
hrad / horod

What puzzles me is the way this seems to cut across the standard linguistic
groupings, with Russian / Ukrainian in an Eastern group and Polish/Czech
classified as Western. It would seem more logical to me to have a "G group"
and an "H" group (although I have a vague worry this would split Sorbian
down the middle).

Piotr might shoot me for saying this, but Polish and Ukrainian strike me as
partciularly close - after a 3 month cassette course in Polish, I could
easly read Ukrainian web sites. It surprises me to see these two languages
classified as being in different branches of the Slav group.

Can anyone shed light on what higher criteria separate the East and Western
Slav groups? Presumably, to believe the traditional split, you would have to
beleive that the g to h split happened subsequently and independently on the
two branches. This is not wholly unbelievable, as the same shift also occurs
between English and Dutch - this obviously must have happened millenia after
the split of proto-germanic from proto-slavic.

Please forgive any obvious ignorance in my question - I'm an
economist/statistician by trade, not a professional linguist. Most of my
language knowledge has been picked up from holidays. If anyone can recommend
a good book on this sort of thing (languages, not holidays ;-) I'm all ears.