Okay, you almost had it.
Working with a copy of your terrain...
Pick a spot for your city, and select it in the groups list (like a TG) and place it. A dialog box pops up just as you say. Select the field nearest your HQ and use that for the "field that will own these objects". Set the zone as follows, 1 for Bish, 2 for Knit, and 3 for Rook, click OK. Remember select all the cells under this city and use the "Flatten terrain" button. Save and build your terrain.
On a large terrain where you want a second Rook city, say 60 to 70 miles back from the front lines, follow the instructions above except make sure that the airfield (before you set the city) and city are both assigned as zone 6 for Rook for instance. See Skuzzy's zone list post.
Suppose that this Rook airfield is field 91. When you decide to flip A91 from zone 3 to zone 6, go into the zone list, highlight A91 and click the Properties button. Select zone 6 and click OK. This will change the zone for anything owned by A91, it's town and it's spawn points etc, you don't need to change them one at a time. Now when you go to set the city, and assign ownership to A91, zone 6, all will be as it should be. It's also possible that you might be able to simply assign city ownership to A91, zone 3, and then come back and flip it all to zone 6, but I haven't tried it.
Remember, this is all new to me too, so there may be additional details I haven't learned yet.