The 'where' would probably be Ebay. You'd need signifcantly better pictures for vintage, including inside the case back to get any reasonable amount of money (which would also show the gold content). The watch itself looks lovely/barely used though, which is nice. It'll still need a service by whoever buys it (though, its not worth paying to do yourself, as it'll be $400 US or so at minimum).
Looks like there is one for sale already on ebay, roughly 700 GBP, in similar shape (though I'll bet they don't get that), though without the engraving (which, IMO, makes yours worth less).
So where to sell: probably ebay. How: Take a bunch of really good pictures and be willing to wait for someone to want it 😀