(No, I didn't think of the Robocop thing..)
Anyway, traditionally, my cities look like the 1st layout. Maximum 2 square overlap. (comes from Civ2 where other civs ALWAYS built a city between yours - a 1-tile city even! I tried the circular build once, but didn't quite have the hang of it.
But, I do look for other things:
1. Bottlenecks - I may build a city there, build some around it (thus, being a possible FP site - both land and sea units). (sort of like akinkhoo's canal tip).
2. Rivers. Definately a boost for any capital, and increased gold!
3. Culture influence - I may try to work my cities towards another civ, to try an flip theirs.
4. Space Fillers - (inspired by Sulla's "Fill-in-Atsu" city in one of the succession games.

) Usually edges of land that fall outside the OCP pattern. These wind up being "fishing villages", or just a space to use up any would-be wasted production. (i.e., hills that are outside of other city radiuses (radii?)).