Ari wrote:

There is a very large copper wire already going to ground on the city
water meter, can I attach other wires to this large ground wire since
it goes to a true ground?

Yes you can. That is a "grounding electrode conductor", and it is
connected to the panel ground. Get a big copper split-bolt connector
and use it to fasten your new grounding wires to that big wire..

Does the 'ground' truely have to go to the ground in the panel?
Shouldn't any dedicated ground source be just as goodas the panel
ground (such as a ground rod driven in hte ground)?

It has to be electrically equivalent to the panel ground, not "just as
good". IIRC, the panel itself, a grounding electrode conductor (big
wire connecting the panel to a ground electrode), and the metal service
raceway (conduit feeding the main panel, assuming it's metal conduit)
are all OK places to connect your equipment grounding wires.

A long time ago, it was permissible to use the nearest cold water pipe
to make a ground, but no longer (someone might replace part of it with
plastic pipe. Also, the plumber could get electrocuted when he cuts the
metal pipe if there is current flowing thru it due to a fault.)

Best regards,
Bob