ORIGINAL: JohnW
"is it safe to assume that the CG should be somewhere near the thickest part of the wing? Will that always be a safe place to start with our models?" - No. It may seem there is a correlation between wing thickness location and CG, but there isn't.
Ideal CG location is not magic and can be easily computed.
http://adamone.rchomepage.com/cg_calc.htm
John is correct. And making an assumption like this is a good way to get in trouble quickly. There is a saying that goes "A nose heavy plane flies poorly, a tail heavy plane flies - once". Getting the CG wrong because of an assumption is a good way to take off with a tail heavy plane that is quite likely uncontrollable.
Ken