If you wait to perform a run-up at the end of a taxiway at a busy airport you will probably not make many friends. Some airports may have designated run-up areas or have runways designated for general aviation but at those that don't would it be acceptable to do a run-up on the ramp before you taxi?
In my humble opinion it is best to ask the FBO for their practices or do it at the ramp with precautions as not to hurt or disturb anyone or anything.
On the Taxi way you might run into difficulties returning to the ramp in case something does not look or perform right during run-up. When in dout I ask Ground for advice.
Most airports have a place to pull off left or right near the end of the runway to allow turning towards the runway (maybe not quite perpindicular at small airports) for the runup before pulling up to the hold short line. If not, there is typically enough room to at least turn & hold short while running up to not blast the guy behind you.
If you have a problem after that, you can likely get clearance to taxi down the runway and pull back nearer to where you started to find an FBO for help. Or back to parking if the FBOs are closed. Non-towered airport, wait for the runway to clear, then announce and pull out and taxi to where needed.
At smaller airports, there will be a place, maybe nearer parking and parallel to the runway, where you can runup before taxiing, or backtaxiing, to the end of the runway for takeoff. 9B1, Marlboro, MA, is one such airport. The paved runup area is above the word MARLBORO, or out in the grass north of the runway.