A few tips that might help. Kindly ensure empty roads for the test.
Roll all the windows up and do not switch on the AC (sorry for making you sweat). Now, turn on the ignition, notice any irregular vibrations. Press the brake pedal to some extent and rev the accelerator. If the car shudders badly, the tranny is weak. Now, let go of the accelerator, let the car idle for a min. Now, rev a little hard (I know it's not good for AT) like picking up a manual in 1st gear. Hear the sound of gear changes happening and try to remember the RPM values at which you hear the gear changes. Stop the car. again rev hard repeat the same and note the RPM markings. Next, rev the car normally and go for a decent spin for a few kms. Turn off the car, open the bonnet and look for any unacceptable burning smells.
Results : If the car revs nicely and even after the above there is no shudder and burnt smells, then upto an extent we can say the the transmission and the engine are healthy. But still, get a professionals opinion for sure for the very reason the 350Z pointed out.
Lastly, best of luck for your AT honda city. It was a gen of a car and if maintained nicely can easily do 2lac kms without any serious issues to the engine and transmission.