Mind you, I'm only a PPL with 30 or so hours since the skills test. So I'm not the absolute authority on this. But I have a personal list of things that I plan on doing, with one of my club instructors, over the next year or two, as and when the occasion arises. And some I've done already. In fact, about half of the things listed here below are activities that are organized by my club by default every year.
1. Advanced stalls (departure stall, turn to final stall), spins, spiral dive, unusual attitude recovery, upset/inverted recovery. Introduction to aerobatics. (Done that. Best 35 minute flight I ever did!)
2. More advanced instrument training (we don't have an IMC rating here, and an IR rating is too big an investment at this point in time). But I would like to fly an ILS, in the soup, a couple of times, and do some more advanced manoeuvres (turning to a heading while climbing/descending), other than the straigh 180 we needed to demo at the skills test.
3. Night VFR rating
4. Basic formation flying
5. Maybe, if the opportunity is there somehow, some flying (landing!) from the right hand seat
6. Precision landing contest (with safety pilot), true engine off landing
7. More varied emergency training. EFATO and various engine failures which make the engine run somewhere between 100% and 0%. How do you land with an engine that surges all the time? Flying (and landing!) on partial (stuck) controls or in an out-of-trim situation.
8. Flying through controlled airspace. (Did that. Transit straight through the Amsterdam Airport Schiphol airspace (class C). Twice now. No problem at all. Very cool. Particularly since I live beneath the EHAM CTR and could fly over my own place this way.)
9. International flight. Crossing the Channel or North Sea. Or worse. (As preparation, I did a sea survival skills training just like the guys from North Sea oil rigs receive. Very cool.)
10. Mountain flying. (Very impractical right now as the highest mountain here is < 1000 ft.)
Furthermore, try to fly as many different types of aircraft as you can. Each aircraft handles differently and needs a slightly different flying technique. Some are flown by the seats of your pants, and some by the numbers, but you have to find the numbers first! Spend a few hours with the POH to learn, at the very least, Vr, Vx, Vy and Vref, T/O and L/D run and distance (MTOW, ISA, 0ft PA, nil wind) and the fuel burn at various cruise settings. Compare them to other aircraft you've flown.
This may be of help for the time that the list of HFD is gone.