incubuspawn,
I'm a marathon player, and if I have no copper nearby, here's what I do:
First, I've usually scouted out a lot of places for moderate or good cities by now. If I'm pushing for rapid expansion, then I may have a 2nd or 3rd city up already.
Second, I try to time my production of a Settler to correspond with the knowledge of such an important resource revealing tech. In the event I do not have the proper resource, this lets me:
Third, settle my new city near (first ring) or on the new resource. I am not above settling on a resource to get it to my empire quicker. This is mostly true for Stone, as it is possible to build a few wonders that have a bonus to stone before researching Masonry. However, I've done this with Iron before, too.
Sure you nerf your city in the third step, but I value my empire over a single city. If moving my city center 2 spaces one direction or the other means my empire becomes that much better so many turns quicker (18 turns to build a Quarry on Marathon!), then I'm all for it.
Also, if you're playing multiplayer, there's nothing wrong with turning off the Barbarians. You'll have plenty of things to fight eventually. :lol;