To add to other answers:
Even in Civ4 building overlapping cities made sense from time to time. A city working all squares (21 pop) was rare even then for me, so it made more sense to win a good (resource) tile for a (new) city, even when that meant it to overlap on some average tiles with another of your cities.
Note also that city distance does not affect anything in Civ5, unlike in Civ4 where you got increased maintenance costs for cities far away.
... to figure out how close to build cities to maximize my territory ...
Personally I more and more get the feeling than maximizing territory isn't as important in Civ5 as it was in previous games. Also, luxury (and strategic) resources are far more important to get than to maximize territory, because it takes ages to get a city to it's maximum radius (unless you culture bomb your way I guess). Buying territory for territory's sake doesn't make sense either, because it gets expensive very quickly.
It still seems that building a new city as soon as you can afford one (you need enough happiness, because building a new city will decrease your overall h.! -- if the new city unlocks a new luxury resource, than can of course help.) is a good strategy in Civ5, but I find that other factors are far more important than if a city overlaps another: Like how can I max out good squares for the new city, without stealing important stuff from an existing city, even if that means to overlap 50% with an already existing one.
To sum up: For territory cohesion I would go 3-4 hexes distance (vs. the 6 maximum) but I would build a city even 12 hexes away, I'd get a good resource for it.