My general rule of thumb is dependent on my short term goals defined by my initial scouting.
If I find that I have plenty or room to rex, I try to grab land and not have overlap. If though, I find I am close to a civ I want to rush, then I will usually settle close and not be worried about overlap at all.
The benefits of this are that I can usually do with one less worker to connect resources and the cities. And the second capital will usually be enough of a payoff that having a city that will have a low potential later is not a big deal.
I saw the benefit in one of Mutineer's games where he had his second city very close to his capital to share horses and food resources.
I do this now too to swap out the tiles to abuse the whip and maximize production/growth while I build a force to take the next civ out in as short a time as possible.
Also, later in game, if my capitol is located inland but there is enough room to grab a seafood resource and work some mines from the capitol, I have no problem settling it. It might not be a big city, but maintenance is not too bad and switching out tiles will help it build granary, lighthouse, library and pump some naval units later if needed.