The same principles and checks apply to any other piece of equipment required for the flight, including maps, procedure charts, frequency tables, checklists, etc. Then make sure that there is nothing loose in the cockpit, including the screws with which instruments are attached to the panel, items located in the modest but nevertheless real cargo bay and so on.
Then look around to see if there are no obstacles around the plane and move all the surface controls; moving the rudder using the pedals may be difficult in these circumstances, but do so with the elevator, ailerons and flaps, if the plane comes with them.
Checking the movement of the right or starboard aileron.
They should move smoothly, with no strange noises or friction, and in the intended direction; this seems odd but there have been cases in which mechanics just messed the command cables and connected them in an inverse fashion. It is unlikely but not impossible, so make sure!
Starboard aileron control cable pulley.
Check that there are sick bags for all occupants (two normally, but if your passenger carries a baby or toddler, make them three or even four; bags don't weight much, after all). Open the fuel valve and move the power level to idle. Then check that both seats have no spurious movement and tidily place both seat belts over the cushions. It is not only a matter of aesthetics but practicality: It will be easier to fasten the seat belts once both of you are sitting there.
Right aileron control cable horn attachment.
Lastly, check that control cables or wires have nothing that impedes their movement, and verify that they are correctly attached; I am referring to the brake and rudder pedals specifically.
Aileron hinge.
Place the wheel chocks and look under the airplane's belly and the right side wheel. This one should have the right air pressure and present to scratches or anything abnormal.Make sure that there are no stains or drops of fluid anywhere on the belly, the landing gear or on the tarmac; anything fluid should be treated as very suspicious.