Every situation is different and you want to consider a few things when picking where to do it including:
Surface (ideally you want a somewhere sealed)
Surroundings (try not to blow crap into a hangar)
Traffic (try not to hold people up on taxi ways or even worse runways)
Warmth (you want your engine to be a little warm, so if you choose to do it at parking position you are sitting there for a long time. You could use the taxi to warm the engine but then you could be blocking someone)
There is no right answer to this, just better ones (there is probably wrong ones though).
Remember run ups and run up or pre take off checks are two different things. You can sit in your parking spot and do all of the checklist except the physical run up. Taxi to the holding point, do an idle check before stopping. Power up, mag check, carby if applicable, pull power back to 1,000 (shouldn't take much longer to do than say). Conduct line up checks. Go. If you detach the run up from the rest of the pre take off checks you make choosing a spot to do it much easier.