OK, stuff one may be doing during a flight:
After takeoff, climb straight ahead until clear of obstacles. Monitor engine performance - must be as per book performance.
Trim forward for the desired climb speed (for engine cooling etc).
Turn onto the GPS track, or fly to he initial waypoint if doing DR.
Climb to desired level; when nearly reached trim forward for desired cruise speed, when this is reached reduce power setting to the correct one for that cruise speed.
During all above steps, look out for traffic. Hard to do during the first bit of the climb, due to pitch attitude. Monitor engine performance.
If using GPS then simply fly the loaded route, otherwise at initial waypoint (which could be the airfield overhead, though this is not a good idea due to traffic) set heading to next waypoint and start stopwatch.
If not using GPS then enroute to the first waypoint, look at indications that the winds aloft forecast is rubbish (ground features appearing too far left/right too early/late) and adjust heading by say 5 degrees. (There are all kinds of clever tricks one can do here but hey this is just a PPL and you buy a GPS for any real flying).
Look out for traffic, while flying the pre-planned route both laterally and vertically. Monitor engine performance, fuel, etc etc. Call up the next appropriate station, or call nobody, but always have the radio tuned to a live station so if you make a mayday call somebody will hear.
With a GPS it is far easier because you get lateral guidance and, assuming it is a good one, you can see your position relative to features on the chart. Using DR, the cockpit workload is high and it is important to be able to fly an accurate heading and speed. Some people enjoy that sort of thing but if going somewhere for real I stick the autopilot on and enjoy the scenery while looking out for traffic and monitoring everything.
VFR, one needs to watch the weather conditions; in general this means remaining below cloud. If the cloudbase gets too low, turn back / divert etc.
One could go on...