I usually play a peaceful style on Monarch level. I try to space out cities such that there is not too much footprint overlap. It works for me, because my game strategies usually don't involve the quick wins, and I do plan to have and use hospitals.
Still, it is better to have overlap than to have wasted tiles. Every tile in your territory should be working for you, if possible.
Plan your cities based not on using the full footprint, but based on which tiles they need to achieve your goals. How many shields of production do I want this city to have in the endgame? The answer is not as many as possible; excess gets wasted. Then, how much population do you need to support the production? Again, you don't want as much population as possible,just enough to support the production. I usually have 13-20 in my core cities; 13 gets me the defensive bonus of a metropolis, and you never need more than 20 to work a full city footprint.
From what I have observed with the AI, city placement is not so much a matter of intentionally cramming cities together. In the middle of a land mass with resources evenly distributed, the AI may do a lot of spacing. Things get crammed together when terrain makes it hard to space the cities, or when certain resources get clumped together (the AI likes to plop cities down right on top of resources), or in the latter stages of city placement when the AI is trying to squeeze out every last remaining tile.
I would definitely not hesitate to break the ring to plant a city at an important choke point or to get a vital resource. Both of those things are probably more important to you in the long run than the corruption savings of the ring. For me, since I'm playing peaceful most of the game, a choke point is vital so that I don't have to build a huge army to defend my country. Getting the extra resource depends on the resource; if it's a luxury or strategic I don't have, it's defintely worth getting. Even if it's a second or third source of a strategic or a luxury, it gives me something to trade.