During your rental period, you can preferably park, lock and unlock the Donkey Republic bicycle at a bicycle rack, as often as you want. That bike can only be used by you and will not be assigned to anyone else during your current rental. You don't have to park it at one of the pick-up locations.
Whenever you want to take a break, just tap "Close" in the Gaiyo app and push down the lock lever to close it. Then use the app again to unlock the bike when you are ready to continue cycling.