How to dismantle my own city
Double click city to bring up the City menu. This should start in the overview tab. Click the settings tab, select "Disband if build settler at size 1" Wait however many turns (make sure it won't grow before it finishes)
The answer by Foon is the proper way to dismantle your own city. Here, I will show a cheat for dismantling your cities.
Press Ctrle to bring up the edit menu (the edit mode).
In the menu, click on the city icon (one of the icons I surrounded with a black box in the image above).
Then, click on the red "X" icon in the menu.
Click on the city itself to remove it from the map.
Exit edit mode by pressing Ctrle.