I have a few parked cities:
*end of chapter 3 - old tech tree, just for fun spire catering city, not a diamond farm since it has no other worlds to share them with loI. All my big cities fight the Spire but I love the Mastermind game, so even though I started this city to test the tournament /spire formula changes, I never went past chapter 3 and negotiate to the top every week to my heart's content.
*end of chapter 7 - almost all the barracks troops have their three star upgrades (minus mortars for humans / treants for elves) and the spire enemies are still two star. At this point my cities are true hybrids, though still leaning towards catering, which I enjoy. Even if I don't park a city here forever, I tend to linger here to upgrade the Bulwark and Monastery/Sanctuary especially, since once you enter chapter 8 the Spire enemies become three star forevermore (for now).
*end of Elementals (chapter 12) - same reason as someone gave earlier, to avoid sentients in the Spire. I was parked here for two-ish years, but finally the lure of Timewarp was too great.
This city will park indefinitely at the end of chapter 15.
*end of chapter 15 (Elvenar) - all the three star troop upgrades are accomplished. Timewarp and Simia Sapiens were unlocked at the end of 14. The two cities that will be parked here indefinitely are in FA - focused fellowships, and chapter 15 had a T1 upgrade, so bracelet-making is more efficient here at the end of the chapter vs the beginning of chapter 16.
*my beta city is lingering at the end of chapter 7, but I'm thinking of eventually parking it in Woodelves (after at least T1 and MH upgrades). Then there's no expiring resources to deal with in the Spire and many pop /culture buildings get a huge boost in the upgrade from orcs to woodelves.
Besides the chapters with Spire reasons, I park at the end of a chapter instead of the beginning mainly for FA /event reasons, since requirements go up for each chapter right at the start. When I'm just lingering between chapters (my two biggest cities take turns going through chapters), I linger at the beginning of the new chapter so any buildings I get are at that chapter level.