7 cities is still less than I'd expect You mentioned Prince in your OP, so I was confused
The risk with 7 cities is that you will always be vulnerable to military incursions. Unless you're playing on a level that permits you to be ahead of everyone else tech-wise, you will not be able to build sufficient military to defend yourself. Admittedly if you play no-aggressive-AI and on a low enough level (prince or below, I suspect), you may not risk problems from this.
Usually, by the mid game, it's good to build 'filler' cities that may well be right in the middle of 'good' cities; they still pay for themselves and can build some military units. Also, coastal 'lighthouse' commerce cities are very valuable - periodically use one or two hammer tiles that is shared with a real city, long enough to build a lighthouse and a library/marketplace, and then just use 2/3 ocean tiles (even better 2/4 with FIN!!).
The risk with 7 cities is that you will always be vulnerable to military incursions. Unless you're playing on a level that permits you to be ahead of everyone else tech-wise, you will not be able to build sufficient military to defend yourself. Admittedly if you play no-aggressive-AI and on a low enough level (prince or below, I suspect), you may not risk problems from this.
Usually, by the mid game, it's good to build 'filler' cities that may well be right in the middle of 'good' cities; they still pay for themselves and can build some military units. Also, coastal 'lighthouse' commerce cities are very valuable - periodically use one or two hammer tiles that is shared with a real city, long enough to build a lighthouse and a library/marketplace, and then just use 2/3 ocean tiles (even better 2/4 with FIN!!).
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