Donut shops are sometimes the only businesses open in overnight hours, and many welcome police officers to stop by, even offering free coffee. Thus police cars were seen at donut shops more often than other random locations.

It's more so that police love (need really) coffee for late shifts or long 12 hour+ shifs. Before Starbucks took over as THE coffee shop it was usually doughnut shops that were open either 24 hours or really early/late for cops to stop in for their coffee fix. Plus doughnuts are easy to eat 'on the go' or in a car as compared to say a burger and less messy. So it was obvious and convenient that when a cop would stop for coffee they would get a doughnut too.
One could go on to make the argument that they are easy to bring in and share to a precinct(in this case) but any sort of job location really with the convince of different flavors for people and their grab one and go size. TL; DR: cops need coffee, coffee shops sell doughnuts. Also doughnuts are amazing who doesn't like them?