Ebay is your best bet. But unfortunately there isn't much demand for that style. So you'd want to target those specifically looking for that one with a BIN or OBO posting. Is it new in box? Used? What's the condition?

It's usually the classic style g shocks (dw5600 & dw6900 form factor) that fetch the most potential buyers and cash.
Price usually corresponds to age (vintage & just released from japan will take the lion's share), rarity, country of manufacture, colorway, and features.

I'd use sold listings as a guideline: Be sure to state the full model number and all that limited edition whodesigned it whatnot.
Casio G Shock Limited Edition Eric Haze Box New 4367 G 304EH 7JR RARE Dee Ricky | eBay
You're going to have to be patient if you don't want to let go of it for pennies on the dollar.
Offer international shipping but absolutely insist that the seller will pay for insured shipping and you report the full amount that the watch sold for sans shipping on the customs forms. There are collectors in Asia willing to pay out the nose for g shocks they want.