I'm looking for a website, like Flight Radar, that can display the positions of aircraft going back a few days (i.e. not a live map)
If you just need a few days then FlightAware let’s you do that. I think it goes back 7 days for free. Past that you have to pay. That is for a particular flight. FR24 has a history feature that will play back the whole radar starting at a particular time. It plays back at 12x speed, though.
On FR24 you just open the main screen, move the map where you want it then click the clock icon on the right side. Enter the time and date you’re interested in. Note that it’s in UTC time, so you’ll have to convert your local time to UTC.
Then it will begin playing back. You can see the time and playback speed on a bar at the bottom of the screen.