I am considering making two unusual districts in the perhaps-to-be-made city. Let's call them Fast Town and Slow Town --- no, the Quick Quarter and the Delay District. The Slow Slum, I hope, is not appropriate.
In the Quick Quarter, time runs nine times faster than outside. One could enter it after breakfast in the regular world, enjoy a full day's worth of whatevers, sleep it off, and leave it at lunchtime in the regular world. Or, one could spend a year in there writing a book, and only the month of Trandary would pass in the regular world. I expect this to be popular with many sorts of people, such as vacationers; we will need to have excellent recreations available within, among other things.
In the Delay District, it runs nine times slower than in normal reality. I don't expect this to be as popular as the Quick Quarter, but if one is working in the Quick Quarter and one does not want to age unduly, one must spend some time in the Delay District.
I could also produce a Quite Quick Quarter and a Doubly Delayed District, eighty-one times faster and slower, for those occasions in which one needs to do a year's worth of work in three days, or ... well, the main use I have thought of is, to wait out an unpleasant term painlessly, such as a statute of limitations, or wait for a rich relative to die. Or, perhaps, if one is under a curse fatal in eighty-one hours, one could go there and hope that the relevant wizards and healers (me, I suppose) could work out a cure in a year -- but this is quite unlikely, since most curses go by days (viz. dawns in the real world) and not by hours.
As far as I know, no other city has such amenities, though certain rooms in certain wizards' manses or ducal palaces work that way. Most people rarely if ever get to have access to time manipulation.
How might you take advantage of one or more of these regions?
What sorts of amenities should we provide in them?
What perils and troubles and problems might arise from them?